結果
| 問題 | No.97 最大の値を求めるくえり |
| コンテスト | |
| ユーザー |
 miscalc
|
| 提出日時 | 2026-10-31 10:27:38 |
| 言語 | C++23 (gcc 15.3.0 + boost 1.92.0 + ACL) |
| 結果 |
AC
不安定
|
| 実行時間 | 380 ms / 5,000 ms |
| + 114µs | |
| コード長 | 69,364 bytes |
| 記録 | |
| コンパイル時間 | 4,298 ms |
| コンパイル使用メモリ | 413,424 KB |
| 実行使用メモリ | 9,812 KB |
| 最終ジャッジ日時 | 2026-10-31 10:27:53 |
| 合計ジャッジ時間 | 14,853 ms |
|
ジャッジサーバーID （参考情報） |
judge2_0 / judge7_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 19 |
ソースコード
#define SINGLE_TESTCASE
// #define MULTI_TESTCASE
// #define AOJ_TESTCASE
#define FAST_IO
// #define FAST_CIO
// #define INTERACTIVE
#define INF 4'000'000'000'000'000'037LL
#define EPS 1e-11
// https://github.com/miscalculation53/library/tree/wip/template/template_all.hpp
// https://github.com/miscalculation53/library/tree/wip/template/template_all_but_modint.hpp
// https://github.com/miscalculation53/library/tree/wip/template/template_types.hpp
#include <bits/stdc++.h>
using namespace std;
// https://github.com/miscalculation53/library/tree/wip/template/template_float128.hpp
using namespace std;
#if __cplusplus > 202002L && defined(__STDCPP_FLOAT128_T__)
#include <stdfloat>
using f128 = std::float128_t;
#elif defined(__SIZEOF_FLOAT128__)
using f128 = __float128;
#else
#error "f128 requires a compiler with IEEE binary128 support, such as GCC on x86_64."
#endif
#define LIBRARY_HAS_FLOAT128 1
#if __cplusplus > 202002L && defined(__STDCPP_FLOAT128_T__) && \
(defined(_GLIBCXX_HAVE_FLOAT128_MATH) || defined(_GLIBCXX_LDOUBLE_IS_IEEE_BINARY128))
#define LIBRARY_USE_QUADMATH 0
#else
#include <quadmath.h>
#define LIBRARY_USE_QUADMATH 1
//! https://gcc.gnu.org/onlinedocs/libquadmath/Math-Library-Routines.html
#define _p_F128_UNARY(name) \
inline f128 name(f128 x) { return f128(name##q(__float128(x))); }
_p_F128_UNARY(acos)
_p_F128_UNARY(acosh)
_p_F128_UNARY(asin)
_p_F128_UNARY(asinh)
_p_F128_UNARY(atan)
_p_F128_UNARY(atanh)
_p_F128_UNARY(cbrt)
_p_F128_UNARY(ceil)
_p_F128_UNARY(cos)
_p_F128_UNARY(cosh)
_p_F128_UNARY(erf)
_p_F128_UNARY(erfc)
_p_F128_UNARY(exp)
_p_F128_UNARY(exp2)
_p_F128_UNARY(expm1)
_p_F128_UNARY(fabs)
_p_F128_UNARY(floor)
_p_F128_UNARY(lgamma)
_p_F128_UNARY(log)
_p_F128_UNARY(log10)
_p_F128_UNARY(log1p)
_p_F128_UNARY(log2)
_p_F128_UNARY(logb)
_p_F128_UNARY(nearbyint)
_p_F128_UNARY(rint)
_p_F128_UNARY(round)
_p_F128_UNARY(sin)
_p_F128_UNARY(sinh)
_p_F128_UNARY(sqrt)
_p_F128_UNARY(tan)
_p_F128_UNARY(tanh)
_p_F128_UNARY(tgamma)
_p_F128_UNARY(trunc)
#undef _p_F128_UNARY
#define _p_F128_BINARY(name) \
inline f128 name(f128 x, f128 y) { return f128(name##q(__float128(x), __float128(y))); } \
template <class T, enable_if_t<is_arithmetic_v<T>, int> = 0> \
inline f128 name(f128 x, T y) { return name(x, f128(y)); } \
template <class T, enable_if_t<is_arithmetic_v<T>, int> = 0> \
inline f128 name(T x, f128 y) { return name(f128(x), y); }
_p_F128_BINARY(atan2)
_p_F128_BINARY(copysign)
_p_F128_BINARY(fdim)
_p_F128_BINARY(fmax)
_p_F128_BINARY(fmin)
_p_F128_BINARY(fmod)
_p_F128_BINARY(hypot)
_p_F128_BINARY(nextafter)
_p_F128_BINARY(pow)
_p_F128_BINARY(remainder)
#undef _p_F128_BINARY
inline f128 fma(f128 x, f128 y, f128 z)
{ return f128(fmaq(__float128(x), __float128(y), __float128(z))); }
inline f128 hypot(f128 x, f128 y, f128 z)
{ return hypot(hypot(x, y), z); }
namespace template_float128_detail
{
template <class T>
constexpr bool arithmetic = is_arithmetic_v<T> || is_same_v<T, f128>;
}
#define _p_F128_TERNARY_MIXED(name) \
template <class T, class U, enable_if_t<template_float128_detail::arithmetic<T> && template_float128_detail::arithmetic<U>, int> = 0> \
inline f128 name(f128 x, T y, U z) { return name(x, f128(y), f128(z)); } \
template <class T, class U, enable_if_t<template_float128_detail::arithmetic<T> && !is_same_v<T, f128> && template_float128_detail::arithmetic<U>, int> = 0> \
inline f128 name(T x, f128 y, U z) { return name(f128(x), y, f128(z)); } \
template <class T, class U, enable_if_t<template_float128_detail::arithmetic<T> && !is_same_v<T, f128> && template_float128_detail::arithmetic<U> && !is_same_v<U, f128>, int> = 0> \
inline f128 name(T x, U y, f128 z) { return name(f128(x), f128(y), z); }
inline f128 ldexp(f128 x, int exponent)
{ return f128(ldexpq(__float128(x), exponent)); }
inline f128 scalbn(f128 x, int exponent)
{ return f128(scalbnq(__float128(x), exponent)); }
inline f128 scalbln(f128 x, long exponent)
{ return f128(scalblnq(__float128(x), exponent)); }
inline f128 modf(f128 x, f128 *integer)
{
__float128 value;
const auto fraction = modfq(__float128(x), &value);
*integer = f128(value);
return f128(fraction);
}
inline f128 remquo(f128 x, f128 y, int *quotient)
{ return f128(remquoq(__float128(x), __float128(y), quotient)); }
inline long lrint(f128 x) { return lrintq(__float128(x)); }
inline long lround(f128 x) { return lroundq(__float128(x)); }
inline long long llrint(f128 x) { return llrintq(__float128(x)); }
inline long long llround(f128 x) { return llroundq(__float128(x)); }
inline int ilogb(f128 x) { return ilogbq(__float128(x)); }
#endif
inline f128 nexttoward(f128 x, long double y)
{ return nextafter(x, f128(y)); }
namespace template_float128_detail
{
inline bool parse(string_view s, f128 &x)
{
if (!s.empty() && s.front() == '+')
{
s.remove_prefix(1);
if (s.empty() || s.front() == '-') return false;
}
#if LIBRARY_USE_QUADMATH
string token(s);
char *end;
errno = 0;
const __float128 value = strtoflt128(token.c_str(), &end);
if (end == token.data() || end != token.data() + token.size()) return false;
if (errno == ERANGE && (value == 0 || isinfq(value))) return false;
x = f128(value);
return true;
#else
auto [p, ec] = from_chars(s.data(), s.data() + s.size(), x);
return ec == errc{} && p == s.data() + s.size();
#endif
}
inline string format(f128 x, chars_format style, int precision)
{
string s(128, '\0');
while (true)
{
#if LIBRARY_USE_QUADMATH
const char *spec = style == chars_format::fixed ? "%.*Qf" :
style == chars_format::scientific ? "%.*Qe" : "%.*Qg";
const int n = quadmath_snprintf(s.data(), s.size(), spec, precision, __float128(x));
if (n < 0) abort();
if (size_t(n) < s.size())
{
s.resize(size_t(n));
return s;
}
s.resize(size_t(n) + 1);
#else
auto [p, ec] = to_chars(s.data(), s.data() + s.size(), x, style, precision);
if (ec == errc{})
{
s.resize(size_t(p - s.data()));
return s;
}
s.resize(s.size() * 2);
#endif
}
}
}
using ld = decltype(EPS);
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
using pll = pair<ll, ll>;
using tlll = tuple<ll, ll, ll>;
using tllll = tuple<ll, ll, ll, ll>;
#define vc vector
template <class T>
using vvc = vc<vc<T>>;
template <class T>
using vvvc = vc<vc<vc<T>>>;
using vb = vc<bool>;
using vl = vc<ll>;
using vpll = vc<pll>;
using vtlll = vc<tlll>;
using vtllll = vc<tllll>;
using vstr = vc<string>;
using vvb = vvc<bool>;
using vvl = vvc<ll>;
template <class T>
using pql = priority_queue<T, vc<T>, greater<T>>;
template <class T>
using pqg = priority_queue<T>;
using i128 = __int128_t;
using u128 = __uint128_t;
i128 stoi128(const string &s)
{
const bool neg = s.front() == '-';
u128 res = 0;
for (size_t i = size_t(neg); i < s.size(); i++)
res = 10 * res + unsigned(s[i] - '0');
if (neg)
return -i128(res - 1) - 1;
return i128(res);
}
string i128tos(i128 x)
{
if (x == 0) return "0";
string sign = "", res = "";
u128 ux;
if (x < 0)
ux = u128(-(x + 1)) + 1, sign = "-";
else
ux = u128(x);
while (ux > 0)
{
res += char('0' + ux % 10);
ux /= 10;
}
reverse(res.begin(), res.end());
return sign + res;
}
istream &operator>>(istream &is, i128 &a)
{
string s;
if (!(is >> s)) return is;
a = stoi128(s);
return is;
}
ostream &operator<<(ostream &os, const i128 &a)
{
os << i128tos(a);
return os;
}
#define cauto const auto
// https://github.com/miscalculation53/library/tree/wip/template/template_rep.hpp
#define overload4(_1,_2,_3,_4,name,...) name
#define LIBRARY_REPEAT_LOOP(T,i,l,r,d) for (auto [i, library_repeat_end, library_repeat_step] = array<T, 3>{T(l), T(r), T(d)}; library_repeat_step > 0 ? i < library_repeat_end : i > library_repeat_end; i += library_repeat_step)
#define rep1(i,n) LIBRARY_REPEAT_LOOP(ll, i, 0, n, 1)
#define rep2(i,l,r) LIBRARY_REPEAT_LOOP(ll, i, l, r, 1)
#define rep3(i,l,r,d) LIBRARY_REPEAT_LOOP(ll, i, l, r, d)
#define rep(...) overload4(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__)
#define repi1(i,n) LIBRARY_REPEAT_LOOP(int, i, 0, n, 1)
#define repi2(i,l,r) LIBRARY_REPEAT_LOOP(int, i, l, r, 1)
#define repi3(i,l,r,d) LIBRARY_REPEAT_LOOP(int, i, l, r, d)
#define repi(...) overload4(__VA_ARGS__, repi3, repi2, repi1)(__VA_ARGS__)
#define fe(...) for (auto __VA_ARGS__)
#define fec(...) for (cauto &__VA_ARGS__)
#define fem(...) for (auto &__VA_ARGS__)
// https://github.com/miscalculation53/library/tree/wip/template/template_math.hpp
// https://github.com/miscalculation53/library/tree/wip/template/template_arithmetic.hpp
template <class T, class U, class P>
constexpr pair<T, U> &operator+=(pair<T, U> &a, const P &b);
template <class T, class U, class P>
constexpr pair<T, U> operator+(pair<T, U> a, const P &b);
template <class T, class U, class P>
constexpr pair<T, U> &operator-=(pair<T, U> &a, const P &b);
template <class T, class U, class P>
constexpr pair<T, U> operator-(pair<T, U> a, const P &b);
template <class T, class U>
constexpr pair<T, U> operator-(pair<T, U> a);
template <class T, size_t n, class A>
constexpr array<T, n> &operator+=(array<T, n> &a, const A &b);
template <class T, size_t n, class A>
constexpr array<T, n> operator+(array<T, n> a, const A &b);
template <class T, size_t n, class A>
constexpr array<T, n> &operator-=(array<T, n> &a, const A &b);
template <class T, size_t n, class A>
constexpr array<T, n> operator-(array<T, n> a, const A &b);
template <class T, size_t n>
constexpr array<T, n> operator-(array<T, n> a);
template <class... Ts, class Tp>
constexpr tuple<Ts...> &operator+=(tuple<Ts...> &a, const Tp &b);
template <class... Ts, class Tp>
constexpr tuple<Ts...> operator+(tuple<Ts...> a, const Tp &b);
template <class... Ts, class Tp>
constexpr tuple<Ts...> &operator-=(tuple<Ts...> &a, const Tp &b);
template <class... Ts, class Tp>
constexpr tuple<Ts...> operator-(tuple<Ts...> a, const Tp &b);
template <class... Ts>
constexpr tuple<Ts...> operator-(tuple<Ts...> a);
namespace internal
{
};
// https://github.com/miscalculation53/library/tree/wip/utils/is_integral_ext.hpp
template <class T>
constexpr bool is_integral_ext = is_integral_v<T> || is_same_v<T, i128> || is_same_v<T, u128>;
template <class T>
constexpr bool is_signed_ext = is_signed_v<T> || is_same_v<T, i128>;
template <class T>
constexpr bool is_unsigned_ext = is_unsigned_v<T> || is_same_v<T, u128>;
// https://github.com/miscalculation53/library/tree/wip/utils/integer_arithmetic.hpp
// https://github.com/miscalculation53/library/tree/wip/utils/make_unsigned_ext.hpp
template <class T>
struct make_unsigned_ext
{
using type = make_unsigned_t<T>;
};
template <>
struct make_unsigned_ext<i128>
{
using type = u128;
};
template <>
struct make_unsigned_ext<u128>
{
using type = u128;
};
template <class T>
using make_unsigned_ext_t = typename make_unsigned_ext<T>::type;
template <class T>
struct make_signed_ext
{
using type = make_signed_t<T>;
};
template <>
struct make_signed_ext<u128>
{
using type = i128;
};
template <class T>
using make_signed_ext_t = typename make_signed_ext<T>::type;
template <class T>
constexpr bool is_negative(T x)
{
static_assert(is_integral_ext<T>);
if constexpr (is_signed_ext<T>) return x < 0;
return false;
}
template <class T, bool = is_integral_ext<T>>
struct unsigned_arithmetic { using type = T; };
template <class T>
struct unsigned_arithmetic<T, true>
{
static_assert(!is_same_v<T, bool>);
using type = common_type_t<unsigned int, make_unsigned_ext_t<T>>;
};
template <class T>
using unsigned_arithmetic_t = typename unsigned_arithmetic<T>::type;
// https://github.com/miscalculation53/library/tree/wip/utils/default_infty.hpp
template <class T>
constexpr decltype(auto) default_infty();
namespace default_infty_detail
{
template <class T>
struct is_product : false_type {};
template <class T, class U>
struct is_product<pair<T, U>> : true_type {};
template <class... Ts>
struct is_product<tuple<Ts...>> : true_type {};
template <class T, size_t n>
struct is_product<array<T, n>> : true_type {};
template <class T, class = void>
struct has_infty : false_type {};
template <class T>
struct has_infty<T, void_t<decltype(T::infty())>> : true_type {};
template <class T>
inline constexpr bool unsupported = false;
}
namespace template_math_detail
{
}
template <class T = ll, class U, class V, typename = enable_if_t<is_integral_ext<U> && is_integral_ext<V>>>
inline constexpr T safemod(U a, V b)
{
const T x = T(a), y = T(b);
if constexpr (is_signed_ext<T>)
if (y == T(-1)) return T(0);
const T r = x % y;
return r != T(0) && is_negative(x) != is_negative(y) ? T(r + y) : r;
}
template <class T = ll, class U, class V>
constexpr T ipow(U a, V b)
{
assert(b >= 0);
if (b == 0)
return 1;
if (a == 0 || a == 1)
return a;
if (a < 0 && a == -1)
return b & 1 ? -1 : 1;
T res = 1, tmp = a;
while (true)
{
if (b & 1)
res *= tmp;
b >>= 1;
if (b == 0)
break;
tmp *= tmp;
}
return res;
}
//! https://misawa.github.io/others/avoid_errors/techniques_to_avoid_errors.html
// https://github.com/miscalculation53/library/tree/wip/template/template_vector.hpp
#define ALL(a) (a).begin(), (a).end()
template <class T = ll, class V>
inline T SZ(const V &x) { return x.size(); }
#define eb emplace_back
#define LMD(x,fx) ([&](const auto &x) { return fx; })
#define GEN_VEC(n,i,fi) (gen_vec(n, LMD(i, fi)))
namespace template_vector_detail
{
template <class T, size_t depth>
struct nested_vector
{
using type = vc<typename nested_vector<T, depth - 1>::type>;
};
template <class T>
struct nested_vector<T, 0>
{
using type = T;
};
}
// https://github.com/miscalculation53/library/tree/wip/template/template_algo.hpp
// https://github.com/miscalculation53/library/tree/wip/utils/resolved_infty.hpp
// https://github.com/miscalculation53/library/tree/wip/utils/resolved_value.hpp
template <class T>
vvc<T> top(const vvc<T> &a)
{
if (a.empty())
return {};
const int n = a.size(), m = a[0].size();
vvc<T> b(m, vc<T>(n));
repi(i, n)
{
assert(SZ<int>(a[i]) == m);
repi(j, m) b[j][i] = a[i][j];
}
return b;
}
vstr top(const vstr &a)
{
vvc<char> a_(a.size());
repi(i, SZ<int>(a)) a_[i] = {ALL(a[i])};
vvc<char> b_ = top(a_);
vstr b(b_.size());
repi(i, SZ<int>(b)) b[i] = {ALL(b_[i])};
return b;
}
template <class T, class = void>
struct has_e0 : false_type {};
template <class T>
struct has_e0<T, void_t<decltype(T::e0())>> : true_type {};
template <class T>
inline constexpr bool has_e0_v = has_e0<T>::value;
template <class T>
struct MonoidAdd
{
using S = T;
};
template <class T, auto infty = nullptr>
struct MonoidMin
{
using S = T;
};
template <class T, auto infty = nullptr>
struct MonoidMax
{
using S = T;
};
namespace internal
{
template <class M, class I, class = void>
struct HasMonoidPow : false_type
{
};
template <class M, class I>
struct HasMonoidPow<M, I, void_t<decltype(M::pow(declval<const typename M::S &>(), declval<I>()))>> : true_type
{
};
}
constexpr array<pll, 4> DRULgrid = {{{1, 0}, {0, 1}, {-1, 0}, {0, -1}}};
constexpr array<pll, 4> DRULplane = {{{0, -1}, {1, 0}, {0, 1}, {-1, 0}}};
// https://github.com/miscalculation53/library/tree/wip/template/template_binsearch.hpp
template <class T>
struct is_random_access_iterator
{
static constexpr bool value = is_same_v<
typename iterator_traits<T>::iterator_category,
random_access_iterator_tag
>;
};
template <class T>
constexpr bool is_random_access_iterator_v = is_random_access_iterator<T>::value;
#define DEFAULT_COMP ranges::less
namespace internal
{
};
// https://github.com/miscalculation53/library/tree/wip/template/template_bit.hpp
template <class T>
inline constexpr ull MASK(T k) { return (1ULL << k) - 1ULL; }
inline constexpr ll bit_width(ll x) { return std::bit_width((ull)x); }
inline constexpr ll bit_floor(ll x) { return std::bit_floor((ull)x); }
inline constexpr ll bit_ceil(ll x) { return std::bit_ceil((ull)x); }
inline constexpr ll countr_zero(ll x) { assert(x != 0); return std::countr_zero((ull)x); }
inline constexpr ll popcount(ll x) { return std::popcount((ull)x); }
inline constexpr bool has_single_bit(ll x) { return std::has_single_bit((ull)x); }
inline constexpr ull lsb_pos(ull x) { assert(x != 0); return countr_zero(x); }
inline constexpr ull msb_pos(ull x) { assert(x != 0); return bit_width(x) - 1; }
inline constexpr ull lsb_mask(ull x) { assert(x != 0); return x & -x; }
inline constexpr ull msb_mask(ull x) { assert(x != 0); return bit_floor(x); }
inline constexpr bool btest(ull x, uint k) { return (x >> k) & 1; }
inline constexpr bool bsubset(ull x, ull y) { return (x & y) == x; }
inline constexpr bool bsupset(ull x, ull y) { return (x & y) == y; }
inline constexpr ull bsetminus(ull x, ull y) { return x & ~y; }
// https://github.com/miscalculation53/library/tree/wip/template/template_inout.hpp
// https://github.com/miscalculation53/library/tree/wip/template/template_dump.hpp
#if defined(LOCAL) && LIBRARY_HAS_FLOAT128
namespace cpp_dump::_detail
{
struct export_command;
inline string export_var(const f128 &, const string &, size_t,
size_t, bool, const export_command &);
}
#endif
// https://github.com/miscalculation53/library/tree/wip/template/template_dump_map.hpp
#define CPP_DUMP_DEFINE_DATA(...)
#define dump(...) ((void)0)
#define local(...)
#define oj(...) __VA_ARGS__
#define local_oj(a,b) (b)
#if LIBRARY_HAS_FLOAT128
inline istream &operator>>(istream &is, f128 &x)
{
string s;
if (is >> s)
{
f128 value;
if (template_float128_detail::parse(s, value)) x = value;
else is.setstate(ios::failbit);
}
return is;
}
inline ostream &operator<<(ostream &os, f128 x)
{
const auto field = os.flags() & ios::floatfield;
const auto format = field == ios::fixed ? chars_format::fixed :
field == ios::scientific ? chars_format::scientific : chars_format::general;
string s = template_float128_detail::format(x, format, int(os.precision()));
if ((os.flags() & ios::showpos) && !signbit(x)) s.insert(s.begin(), '+');
if (os.flags() & ios::uppercase)
for (char &c : s) c = char(toupper(static_cast<unsigned char>(c)));
return os << s;
}
#endif
namespace fastio
{
constexpr uint32_t SIZ = 1 << 17;
inline char ibuf[SIZ + 1], obuf[SIZ];
inline uint32_t pil = 0, pir = 0, por = 0;
__attribute__((noinline)) inline void load()
{
const uint32_t remaining = pir - pil;
if (remaining && pil) memmove(ibuf, ibuf + pil, remaining);
pil = 0;
pir = remaining + uint32_t(fread(ibuf + remaining, 1, SIZ - remaining, stdin));
ibuf[pir] = '\x7f';
}
inline bool ascii_space(unsigned char c)
{
return c == ' ' || unsigned(c - '\t') < 5;
}
inline void find_token()
{
for (;;)
{
const char *p = ibuf + pil;
const char *end = ibuf + pir;
while (ascii_space(*p)) ++p;
pil = uint32_t(p - ibuf);
if (p != end) return;
load();
if (!pir) abort();
}
}
__attribute__((noinline)) inline void flush()
{
size_t written = 0;
while (written < por)
{
const size_t n = fwrite(obuf + written, 1, por - written, stdout);
if (!n) abort();
written += n;
}
por = 0;
}
inline void append_bytes(const char *data, size_t size)
{
while (size)
{
const size_t n = min(size, size_t(SIZ - por));
memcpy(obuf + por, data, n);
por += uint32_t(n);
data += n;
size -= n;
if (por == SIZ) flush();
}
}
inline void append_char(char c)
{
if (por == SIZ) flush();
obuf[por++] = c;
}
template <class T>
using integer_magnitude = conditional_t<(sizeof(T) > sizeof(ull)), u128,
conditional_t<(sizeof(T) > sizeof(uint)), ull, uint>>;
inline uint decode_eight(uint64_t columns)
{
columns &= 0x0f0f0f0f0f0f0f0fULL;
const uint64_t pairs = (columns & 0x00ff00ff00ff00ffULL) * 10
+ ((columns >> 8) & 0x00ff00ff00ff00ffULL);
const uint64_t quads = (pairs & 0x0000ffff0000ffffULL) * 100
+ ((pairs >> 16) & 0x0000ffff0000ffffULL);
return uint(quads) * 10000 + uint(quads >> 32);
}
inline constexpr uint powers_of_ten[8] = {1, 10, 100, 1000, 10000, 100000, 1000000, 10000000};
template <class T>
__attribute__((always_inline)) inline void rd1_integer(T &x)
{
using U = integer_magnitude<T>;
const char *p = ibuf + pil;
for (;;)
{
while (ascii_space(*p)) ++p;
if (p != ibuf + pir) break;
pil = pir;
load();
if (!pir) abort();
p = ibuf;
}
bool negative = false;
if (*p == '+') ++p;
else if constexpr (numeric_limits<T>::is_signed)
{
if (*p == '-') negative = true, ++p;
}
U value = 0;
for (;;)
{
while (size_t(ibuf + pir - p) >= 8)
{
uint64_t columns;
memcpy(&columns, p, 8);
const uint64_t stop = ((columns + 0x4646464646464646ULL) |
(columns - 0x3030303030303030ULL)) & 0x8080808080808080ULL;
if (stop)
{
if constexpr (sizeof(U) > sizeof(ull))
{
const unsigned digits = unsigned(__builtin_ctzll(stop)) / 8;
if (digits)
{
uint tail;
if (digits <= 3)
{
tail = unsigned(p[0] - '0');
if (digits >= 2) tail = tail * 10 + unsigned(p[1] - '0');
if (digits == 3) tail = tail * 10 + unsigned(p[2] - '0');
}
else tail = decode_eight(columns << (8 * (8 - digits)));
value = value * powers_of_ten[digits] + tail;
p += digits;
}
goto integer_complete;
}
else
{
if (stop & 0x80808080ULL)
{
if (!(stop & 0x808080ULL))
{
value = value * 1000 + uint(columns & 15) * 100
+ uint(columns >> 8 & 15) * 10 + uint(columns >> 16 & 15);
p += 3;
}
else if (!(stop & 0x8080ULL))
{
value = value * 100 + uint(columns & 15) * 10 + uint(columns >> 8 & 15);
p += 2;
}
else if (!(stop & 0x80ULL))
{
value = value * 10 + uint(columns & 15);
++p;
}
goto integer_complete;
}
break;
}
}
columns &= 0x0f0f0f0f0f0f0f0fULL;
const uint64_t pairs = (columns & 0x00ff00ff00ff00ffULL) * 10
+ ((columns >> 8) & 0x00ff00ff00ff00ffULL);
const uint64_t quads = (pairs & 0x0000ffff0000ffffULL) * 100
+ ((pairs >> 16) & 0x0000ffff0000ffffULL);
value = value * 100000000 + uint(quads) * 10000 + uint(quads >> 32);
p += 8;
}
while (unsigned(*p - '0') < 10)
{
value = value * 10 + unsigned(*p - '0');
++p;
}
pil = uint32_t(p - ibuf);
if (pil != pir) break;
load();
p = ibuf;
if (!pir) break;
}
integer_complete:
pil = uint32_t(p - ibuf);
if constexpr (numeric_limits<T>::is_signed)
{
if (negative && value) x = T(-T(value - 1) - 1);
else x = T(value);
}
else x = T(value);
}
template <class T, enable_if_t<numeric_limits<T>::is_integer, int> = 0>
__attribute__((always_inline)) inline void rd1(T &x) { rd1_integer(x); }
inline void rd1(char &x)
{
find_token();
x = ibuf[pil++];
}
inline void rd1(string &x)
{
find_token();
x.clear();
for (;;)
{
const char *p = ibuf + pil;
const char *end = ibuf + pir;
const char *first = p;
while (p != end && !ascii_space(*p)) ++p;
x.append(first, size_t(p - first));
pil = uint32_t(p - ibuf);
if (p != end) return;
load();
if (!pir) return;
}
}
template <class T>
void rd1_real(T &x)
{
string token;
rd1(token);
const char *first = token.data();
const char *last = first + token.size();
if (first != last && *first == '+') ++first;
auto result = from_chars(first, last, x, chars_format::general);
if (result.ec != errc{} || result.ptr != last)
{
char *end;
if constexpr (is_same_v<T, float>) x = strtof(token.c_str(), &end);
else if constexpr (is_same_v<T, double>) x = strtod(token.c_str(), &end);
else x = strtold(token.c_str(), &end);
if (end != token.data() + token.size()) abort();
}
}
inline void rd1(float &x) { rd1_real(x); }
inline void rd1(double &x) { rd1_real(x); }
inline void rd1(long double &x) { rd1_real(x); }
#if LIBRARY_HAS_FLOAT128
inline void rd1(f128 &x)
{
string token;
rd1(token);
if (!template_float128_detail::parse(token, x)) abort();
}
#endif
template <class A, class B> void rd1(pair<A, B> &x);
template <class... T> void rd1(tuple<T...> &x);
template <class T, size_t N> void rd1(array<T, N> &x);
template <class T> void rd1(vc<T> &x);
inline constexpr auto decimal_triplets = []
{
array<array<char, 3>, 1000> result{};
for (unsigned i = 0; i < 1000; ++i)
{
result[i][0] = char('0' + i / 100);
result[i][1] = char('0' + i / 10 % 10);
result[i][2] = char('0' + i % 10);
}
return result;
}();
inline void store_nine(char *out, uint x)
{
const uint q = x / 1000, r = q / 1000;
memcpy(out, decimal_triplets[r].data(), 3);
memcpy(out + 3, decimal_triplets[q - r * 1000].data(), 3);
memcpy(out + 6, decimal_triplets[x - q * 1000].data(), 3);
}
inline char *prepend_small(char *end, uint x)
{
while (x >= 1000)
{
const uint q = x / 1000;
end -= 3;
memcpy(end, decimal_triplets[x - q * 1000].data(), 3);
x = q;
}
const unsigned digits = 1 + unsigned(x >= 10) + unsigned(x >= 100);
end -= digits;
memcpy(end, decimal_triplets[x].data() + 3 - digits, digits);
return end;
}
inline char *prepend_wide(char *end, ull x)
{
while (x >= 1000000000ULL)
{
const ull q = x / 1000000000ULL;
end -= 9;
store_nine(end, uint(x - q * 1000000000ULL));
x = q;
}
return prepend_small(end, uint(x));
}
inline char *store_leading_triplet(char *out, uint x)
{
if (x >= 100)
{
memcpy(out, decimal_triplets[x].data(), 3);
return out + 3;
}
if (x >= 10)
{
memcpy(out, decimal_triplets[x].data() + 1, 2);
return out + 2;
}
*out = char('0' + x);
return out + 1;
}
inline char *store_short(char *out, uint x)
{
if (x >= 1000000)
{
const uint q = x / 1000000;
const uint r = x - q * 1000000;
out = store_leading_triplet(out, q);
memcpy(out, decimal_triplets[r / 1000].data(), 3);
memcpy(out + 3, decimal_triplets[r % 1000].data(), 3);
return out + 6;
}
if (x >= 1000)
{
const uint q = x / 1000;
out = store_leading_triplet(out, q);
memcpy(out, decimal_triplets[x - q * 1000].data(), 3);
return out + 3;
}
return store_leading_triplet(out, x);
}
template <class U>
inline char *store_ordinary(char *out, U x)
{
if constexpr (sizeof(U) > sizeof(uint))
{
if (x >= 1000000000000000000ULL)
{
const uint hi = uint(x / 1000000000000000000ULL);
const ull tail = x - ull(hi) * 1000000000000000000ULL;
const uint middle = uint(tail / 1000000000ULL);
out = store_leading_triplet(out, hi);
store_nine(out, middle);
store_nine(out + 9, uint(tail - ull(middle) * 1000000000ULL));
return out + 18;
}
}
if (x >= 1000000000)
{
const uint hi = uint(x / 1000000000);
out = store_short(out, hi);
store_nine(out, uint(x - U(hi) * 1000000000));
return out + 9;
}
return store_short(out, uint(x));
}
template <class T, bool newline = false>
__attribute__((always_inline)) inline void wt1_integer(T x)
{
using U = integer_magnitude<T>;
U magnitude = U(x);
bool negative = false;
if constexpr (numeric_limits<T>::is_signed)
{
negative = x < 0;
const U sign_mask = U(0) - U(negative);
magnitude = (magnitude ^ sign_mask) + U(negative);
}
if constexpr (sizeof(U) <= sizeof(ull))
{
if (por > SIZ - 40) flush();
char *out = obuf + por;
*out = '-';
out += negative;
out = store_ordinary(out, magnitude);
if constexpr (newline) *out++ = '\n';
por = uint32_t(out - obuf);
return;
}
char text[48];
char *const end = text + sizeof(text);
char *first = end;
if constexpr (sizeof(U) > sizeof(ull))
{
constexpr ull base = 1000000000000000000ULL;
while (magnitude >= base)
{
const U q = magnitude / base;
const ull tail = ull(magnitude - q * base);
const uint hi = uint(tail / 1000000000ULL);
first -= 18;
store_nine(first, hi);
store_nine(first + 9, uint(tail - ull(hi) * 1000000000ULL));
magnitude = q;
}
first = prepend_wide(first, ull(magnitude));
}
else if constexpr (sizeof(U) > sizeof(uint)) first = prepend_wide(first, magnitude);
else first = prepend_small(first, magnitude);
if (negative) *--first = '-';
append_bytes(first, size_t(end - first));
if constexpr (newline) append_char('\n');
}
inline void wt1(char x) { append_char(x); }
inline void wt1(const char *x) { append_bytes(x, strlen(x)); }
inline void wt1(string_view x) { append_bytes(x.data(), x.size()); }
inline void wt1(const string &x) { append_bytes(x.data(), x.size()); }
template <class T>
void wt1_real(T x)
{
char text[numeric_limits<T>::max_exponent10 + 64];
auto result = to_chars(text, text + sizeof(text), x, chars_format::fixed, 15);
if (result.ec != errc{}) abort();
append_bytes(text, size_t(result.ptr - text));
}
inline void wt1(float x) { wt1_real(x); }
inline void wt1(double x) { wt1_real(x); }
inline void wt1(long double x) { wt1_real(x); }
#if LIBRARY_HAS_FLOAT128
inline void wt1(f128 x)
{
wt1(template_float128_detail::format(x, chars_format::fixed, 35));
}
#endif
template <class A, class B> void wt1(const pair<A, B> &x);
template <class... T> void wt1(const tuple<T...> &x);
template <class T, size_t N> void wt1(const array<T, N> &x);
template <class T> void wt1(const vc<T> &x);
template <class... T>
void read(T &...x) { (rd1(x), ...); }
template <class... T>
void write(T &&...x) { (wt1(forward<T>(x)), ...); }
template <class... T>
void print(T &&...x)
{
if constexpr (sizeof...(T) == 1 &&
((is_integral_v<decay_t<T>> && !is_same_v<decay_t<T>, char>) && ...))
(wt1_integer<decay_t<T>, true>(forward<T>(x)), ...);
else
{
size_t index = 0;
((index++ ? void(append_char(' ')) : void(), wt1(forward<T>(x))), ...);
append_char('\n');
}
}
}
struct Dummy {
Dummy() { atexit(fastio::flush); }
} dummy;
//! https://trap.jp/post/1224/
namespace internal
{
template <class... Ts>
void READnodump(Ts &...a) { fastio::read(a...); }
};
#define READ(...) internal::READnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define LIBRARY_INOUT_TYPE(...) LIBRARY_INOUT_TYPE_IMPL(__VA_ARGS__)(__VA_ARGS__)
#define LIBRARY_INOUT_TYPE_IMPL(T,...) LIBRARY_INOUT_TYPE_SELECT(LIBRARY_INOUT_TYPE_PROBE T, LIBRARY_INOUT_TYPE_KEEP)
#define LIBRARY_INOUT_TYPE_PROBE(...) _, LIBRARY_INOUT_TYPE_REMOVE
#define LIBRARY_INOUT_TYPE_SELECT(...) LIBRARY_INOUT_TYPE_SECOND(__VA_ARGS__)
#define LIBRARY_INOUT_TYPE_SECOND(_0,_1,...) _1
#define LIBRARY_INOUT_TYPE_KEEP(...) __VA_ARGS__
#define LIBRARY_INOUT_TYPE_REMOVE(T) LIBRARY_INOUT_TYPE_KEEP T
#define IN(T,...) LIBRARY_INOUT_TYPE(T) __VA_ARGS__; READ(__VA_ARGS__)
#define CHAR(...) IN(char, __VA_ARGS__)
#define INT(...) IN(int, __VA_ARGS__)
#define LL(...) IN(ll, __VA_ARGS__)
#define STR(...) IN(string, __VA_ARGS__)
#define ARR(T,n,...) array<LIBRARY_INOUT_TYPE(T), n> __VA_ARGS__; READ(__VA_ARGS__)
#define READVEC(...) internal::READVECnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define READVEC2(...) internal::READVEC2nodump(__VA_ARGS__); dump(__VA_ARGS__)
#define VEC(T,n,...) vc<LIBRARY_INOUT_TYPE(T)> __VA_ARGS__; READVEC(n, __VA_ARGS__)
#define VEC2(T,n,m,...) vvc<LIBRARY_INOUT_TYPE(T)> __VA_ARGS__; READVEC2(n, m, __VA_ARGS__)
#define READJAG(...) internal::READJAGnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define JAG(T,n,...) vvc<LIBRARY_INOUT_TYPE(T)> __VA_ARGS__; READJAG(n, __VA_ARGS__)
#define ENDL '\n'
#define WRITE fastio::write
#define PRINT fastio::print
#define PRINTEXIT(...) do { PRINT(__VA_ARGS__); exit(0); } while (false)
#define PRINTRETURN(...) do { PRINT(__VA_ARGS__); return; } while (false)
#define PRINTVEXIT(...) do { PRINTV(__VA_ARGS__); exit(0); } while (false)
#define PRINTVRETURN(...) do { PRINTV(__VA_ARGS__); return; } while (false)
namespace internal
{
};
namespace internal
{
};
#define UNZIP(vt,...) auto [__VA_ARGS__] = unzip(vt)
#define ZIP(vt,...) auto vt = internal::zip_vectors(__VA_ARGS__)
// https://github.com/miscalculation53/library/tree/wip/template/template_random.hpp
mt19937_64 mt;
template <class T = ll, class U1, class U2>
T randrange(U1 l, U2 r)
{
assert(T(l) < T(r));
return uniform_int_distribution<T>(T(l), T(r) - 1)(mt);
}
bool randbool(double p)
{
assert(0 <= p && p <= 1);
return bernoulli_distribution(p)(mt);
}
namespace internal
{
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/template_modint.hpp
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint.hpp
/*!
* Portions corresponding to AtCoder Library (CC0-1.0): modular arithmetic operators.
* Upstream: atcoder/modint.hpp
* https://github.com/atcoder/ac-library/tree/864245a00b00dd008d1abfdc239618fdb7d139da
* License: https://github.com/atcoder/ac-library/blob/864245a00b00dd008d1abfdc239618fdb7d139da/LICENSE
*/
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_static.hpp
// https://github.com/miscalculation53/library/tree/wip/utils/larger_int.hpp
namespace larger_int_detail
{
}
template <class T>
struct larger_int
{
private:
static constexpr bool check();
static_assert(check());
public:
using type = T;
};
#define LARGER_INT(T,U) template <> struct larger_int<T> { using type = U; };
LARGER_INT(signed char, short)
LARGER_INT(short, int)
LARGER_INT(int, long long)
LARGER_INT(long, __int128_t)
LARGER_INT(long long, __int128_t)
LARGER_INT(unsigned char, unsigned short)
LARGER_INT(unsigned short, unsigned int)
LARGER_INT(unsigned int, unsigned long long)
LARGER_INT(unsigned long, __uint128_t)
LARGER_INT(unsigned long long, __uint128_t)
#undef LARGER_INT
template <class T>
struct Rational;
template <class T>
struct larger_int<Rational<T>>
{
using type = Rational<typename larger_int<T>::type>;
};
template <class T>
using larger_int_t = typename larger_int<T>::type;
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_isprime.hpp
/*!
* Portions corresponding to AtCoder Library (CC0-1.0): primality testing.
* Upstream: atcoder/internal_math.hpp
* https://github.com/atcoder/ac-library/tree/864245a00b00dd008d1abfdc239618fdb7d139da
* License: https://github.com/atcoder/ac-library/blob/864245a00b00dd008d1abfdc239618fdb7d139da/LICENSE
*/
namespace internal
{
template <class T>
constexpr ll powmod_constexpr(ll x, ll n, T m)
{
if (m == 1)
return 0;
using U = make_unsigned_t<T>;
using L = larger_int_t<U>;
U r = 1, y = safemod(x, m);
while (n)
{
if (n & 1)
r = L(r) * y % m;
y = L(y) * y % m;
n >>= 1;
}
return r;
}
template <auto n>
constexpr bool isprime = isprime_constexpr(n);
};
namespace internal
{
template <auto M>
struct policy_static
{
using mod_type = decltype(M);
using value_type = make_unsigned_t<mod_type>;
using calc_type = conditional_t<(M <= UINT_MAX), ull, larger_int_t<value_type>>;
static constexpr bool is_prime = isprime_constexpr(M);
static constexpr mod_type mod() { return M; }
static constexpr value_type init(value_type v) { return v; }
static constexpr mod_type val(value_type v) { return v; }
static constexpr value_type mul(value_type a, value_type b)
{
return (value_type)((calc_type(a) * b) % M);
}
};
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_barrett32.hpp
/*!
* Portions corresponding to AtCoder Library (CC0-1.0): Barrett reduction.
* Upstream: atcoder/internal_math.hpp
* https://github.com/atcoder/ac-library/tree/864245a00b00dd008d1abfdc239618fdb7d139da
* License: https://github.com/atcoder/ac-library/blob/864245a00b00dd008d1abfdc239618fdb7d139da/LICENSE
*/
namespace internal
{
struct barrett32
{
uint m = 0;
ull im = 0;
barrett32() = default;
explicit barrett32(uint m) : m(m), im((ull)(-1) / m + 1) {}
uint umod() const { return m; }
uint mul(uint a, uint b) const
{
ull z = a;
z *= b;
ull x = ull((u128(z) * im) >> 64);
ull y = x * m;
return uint(z - y + (z < y ? m : 0));
}
};
template <int id>
struct policy_barrett32
{
using value_type = uint;
using calc_type = ull;
using mod_type = int;
static constexpr bool is_prime = false;
static inline barrett32 reducer{};
static void set_mod(mod_type m)
{
assert(m >= 1 && "modint: set_mod(m) requires m >= 1");
reducer = barrett32(m);
}
static mod_type mod() { return reducer.umod(); }
static value_type umod() { return reducer.umod(); }
static value_type init(value_type v) { return v; }
static mod_type val(value_type v) { return v; }
static value_type mul(value_type a, value_type b) { return reducer.mul(a, b); }
};
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_montgomery64.hpp
namespace internal
{
inline constexpr ull inv64(ull a)
{
ull x = a;
while (a * x != 1) x *= 2 - a * x;
return x;
}
struct montgomery64odd
{
ull m = 0, im = 0, sq = 0;
montgomery64odd() = default;
explicit montgomery64odd(ull m) : m(m), im(inv64(m)), sq(-u128(m) % m) {}
ull umod() const { return m; }
ull reduce(u128 x) const
{
auto t = (x + u128(m) * (-im * ull(x))) >> 64;
if (t >= m) t -= m;
return (ull)t;
}
ull inv_reduce(i128 v) const { return reduce(u128(v % m + m) * sq); }
};
//! https://www.mathenachia.blog/even-mod-montgomery-impl/
struct montgomery64
{
ull m = 0, mx = 0, imx = 0, d = 0, q = 0;
uint b = 0;
montgomery64() = default;
explicit montgomery64(ull m) : m(m)
{
b = countr_zero(m), mx = m >> b;
imx = inv64(mx);
d = powmod_constexpr((mx + 1) / 2, b, mx);
u128 sq = -u128(mx) % mx;
q = (1 + (((sq - 1) * d) << b)) % m;
}
ull umod() const { return m; }
ull reduce(u128 x) const
{
if (b == 0)
{
auto t = (x + u128(mx) * (-imx * ull(x))) >> 64;
if (t >= m) t -= m;
return (ull)t;
}
ull p = x & MASK(b);
x = (x >> b) + p * d;
ull y = p << (64 - b);
auto t = (x + u128(mx) * (imx * (y - ull(x)))) >> (64 - b);
if (t >= m) { t -= m; if (t >= m) t -= m; }
return (ull)t;
}
ull inv_reduce(i128 v) const { return reduce(u128(v % m + m) * q); }
};
template <int id>
struct policy_montgomery64_odd
{
using value_type = ull;
using calc_type = u128;
using mod_type = ll;
static constexpr bool is_prime = false;
static inline montgomery64odd reducer{};
static void set_mod(mod_type m)
{
assert(m >= 1 && m % 2 == 1 && "modint: set_mod(m) requires a positive odd modulus");
reducer = montgomery64odd(m);
}
static mod_type mod() { return reducer.umod(); }
static value_type umod() { return reducer.umod(); }
static value_type init(value_type v) { return reducer.inv_reduce(v); }
static mod_type val(value_type v) { return reducer.reduce(v); }
static value_type mul(value_type a, value_type b) { return reducer.reduce((calc_type)a * b); }
};
template <int id>
struct policy_montgomery64
{
using value_type = ull;
using calc_type = u128;
using mod_type = ll;
static constexpr bool is_prime = false;
static inline montgomery64 reducer{};
static value_type init(value_type v) { return reducer.inv_reduce(v); }
};
};
// https://github.com/miscalculation53/library/tree/wip/math/extgcd.hpp
namespace internal
{
template <class Policy, class PowInv = void>
struct modint_impl
{
using V = typename Policy::value_type;
using M = typename Policy::mod_type;
using mint = modint_impl;
private:
V _v;
public:
static constexpr M mod()
{
M m = Policy::mod();
assert(m > 0 && "modint: modulus is not set; call mint::set_mod(m) before use");
return m;
}
template <class T = Policy>
static auto set_mod(M m) -> decltype(T::set_mod(m)) { return T::set_mod(m); }
modint_impl() : _v(0) { (void)mod(); }
template <class T, typename = enable_if_t<is_integral_ext<T>>>
modint_impl(T v)
{
const V m = mod();
V rem;
if constexpr (is_signed_ext<T>)
{
using S = make_signed_t<V>;
S x = v % S(m);
if (x < 0)
x += m;
rem = x;
}
else
rem = V(v % m);
_v = Policy::init(rem);
};
M val() const { return Policy::val(_v); }
mint &operator+=(const mint &rhs)
{
_v += rhs._v;
if (_v >= Policy::umod())
_v -= Policy::umod();
return *this;
}
mint &operator-=(const mint &rhs)
{
_v -= rhs._v;
if (_v >= Policy::umod())
_v += Policy::umod();
return *this;
}
mint &operator*=(const mint &rhs)
{
_v = Policy::mul(_v, rhs._v);
return *this;
}
template <class T>
mint pow(T n) const
{
assert(n >= 0);
if constexpr (!is_void_v<PowInv>)
return raw(PowInv::get().pow(val(), n));
mint x = *this, r = 1;
while (n)
{
if (n & 1)
r *= x;
x *= x;
n >>= 1;
}
return r;
}
friend mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; }
friend mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; }
friend mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; }
friend mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; }
friend bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; }
friend bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; }
friend M safe_hash_key(const mint &x) { return x.val(); }
friend void rd1(mint &x)
{
long long a;
fastio::rd1(a);
x = a;
}
friend void wt1(const mint &x)
{
fastio::wt1(x.val());
}
};
};
template <int mod>
using static_modint32 = internal::modint_impl<internal::policy_static<mod>>;
template <int id>
using dynamic_modint32 = internal::modint_impl<internal::policy_barrett32<id>>;
template <ll mod>
using static_modint64 = internal::modint_impl<internal::policy_static<mod>>;
template <int id>
using dynamic_modint64_odd = internal::modint_impl<internal::policy_montgomery64_odd<id>>;
template <int id>
using dynamic_modint64 = internal::modint_impl<internal::policy_montgomery64<id>>;
using modint998244353 = static_modint32<998244353>;
using modint1000000007 = static_modint32<1000000007>;
using modint = dynamic_modint32<-1>;
using modint61 = static_modint64<(1LL << 61) - 1>;
using modint64 = dynamic_modint64<-1>;
template <class T>
struct is_modint : std::false_type
{
};
template <class Policy, class PowInv>
struct is_modint<internal::modint_impl<Policy, PowInv>> : std::true_type
{
};
template <class T>
inline constexpr bool is_modint_v = is_modint<T>::value;
template <class T>
struct is_static_modint : false_type {};
template <int m, class PowInv>
struct is_static_modint<internal::modint_impl<internal::policy_static<m>, PowInv>> : true_type {};
template <ll m, class PowInv>
struct is_static_modint<internal::modint_impl<internal::policy_static<m>, PowInv>> : true_type {};
template <class T>
inline constexpr bool is_static_modint_v = is_static_modint<T>::value;
template <class T>
struct is_dynamic_modint : false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint32<id>> : true_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint64_odd<id>> : true_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint64<id>> : true_type {};
template <class T>
inline constexpr bool is_dynamic_modint_v = is_dynamic_modint<T>::value;
template <typename, typename = void>
struct has_mod : std::false_type
{
};
template <typename T>
struct has_mod<T, std::void_t<decltype(T::mod())>> : std::true_type
{
};
template <class mint>
struct modint_less
{
};
template <class mint>
struct modint_hash
{
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/power_table.hpp
template <class mint>
struct PowerTable
{
private:
decltype(mint::mod()) mod;
mint base;
vc<mint> pw;
public:
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/binomial.hpp
template <class T>
struct Binomial
{
private:
inline static decltype(T::mod()) mod;
public:
inline static vc<T> fac_, finv_, inv_;
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/stom.hpp
// https://github.com/miscalculation53/library/tree/wip/math/modint/to_rational.hpp
// https://github.com/miscalculation53/library/tree/wip/math/svp2d.hpp
namespace cpp_dump
{
template <class T>
struct rat_value
{
T p, q;
friend ostream &operator<<(ostream &os, const rat_value &x)
{
os << x.p;
if (x.q != 1)
os << '/' << x.q;
return os;
}
};
struct mint_to_rat_fn
{
};
template <class T>
struct rat_object
{
T value;
};
template <class T>
inline constexpr bool rat_is_map = false;
template <class... Args>
inline constexpr bool rat_is_map<std::map<Args...>> = true;
template <class... Args>
inline constexpr bool rat_is_map<std::multimap<Args...>> = true;
template <class... Args>
inline constexpr bool rat_is_map<std::unordered_map<Args...>> = true;
template <class... Args>
inline constexpr bool rat_is_map<std::unordered_multimap<Args...>> = true;
struct rat_closure : std::ranges::range_adaptor_closure<rat_closure>
{
};
constexpr rat_closure rat()
{
return rat_closure{};
}
}
// using mint = modint998244353;
// using mint = modint1000000007;
using mint = static_modint32<100003>;
// using mint = modint;
using bi = Binomial<mint>;
void init()
{
oj(mt.seed(random_device()()));
}
unsigned xor128_x = 123456789, xor128_y = 362436069, xor128_z = 521288629, xor128_w = 88675123;
unsigned xor128() {
unsigned t = xor128_x ^ (xor128_x << 11);
xor128_x = xor128_y; xor128_y = xor128_z; xor128_z = xor128_w;
return xor128_w = xor128_w ^ (xor128_w >> 19) ^ (t ^ (t >> 8));
}
// https://github.com/miscalculation53/library/tree/wip/math/prime/large/order_primitive_root.hpp
// https://github.com/miscalculation53/library/tree/wip/math/prime/prime_power.hpp
template <class P>
struct PrimePower
{
P p;
int e;
P pe;
PrimePower(P p, int e = 1) : p(p), e(e), pe(ipow(p, e)) {}
PrimePower(P p, int e, P pe) : p(p), e(e), pe(pe) {}
};
tuple<int, ll, ll> ord_pow_div(ll n, ll m)
{
assert(m >= 2);
if (m == 2)
{
int e = countr_zero(n);
return {e, 1LL << e, n >> e};
}
if (n % m != 0)
return {0, 1, n};
n /= m;
if (n % m != 0)
return {1, m, n};
n /= m;
ll m2 = m * m;
auto [f, m2f, nn] = ord_pow_div(n, m2);
int e = 2 + 2 * f;
ll me = m2f * m2;
if (nn % m == 0)
e++, me *= m, nn /= m;
return {e, me, nn};
}
template <class P>
vc<PrimePower<P>> factorized_mul
(const vc<PrimePower<P>> &fac1, const vc<PrimePower<P>> &fac2)
{
const int n = fac1.size(), m = fac2.size();
vc<PrimePower<P>> fac;
fac.reserve(n + m);
int i = 0, j = 0;
while (i < n && j < m)
{
if (fac1[i].p < fac2[j].p)
fac.emplace_back(fac1[i++]);
else if (fac1[i].p > fac2[j].p)
fac.emplace_back(fac2[j++]);
else
{
using U = larger_int_t<P>;
fac.emplace_back(fac1[i].p, fac1[i].e + fac2[j].e,
U(fac1[i].pe) * U(fac2[j].pe));
i++, j++;
}
}
fac.insert(fac.end(), fac1.begin() + i, fac1.end());
fac.insert(fac.end(), fac2.begin() + j, fac2.end());
return fac;
}
// https://github.com/miscalculation53/library/tree/wip/math/prime/large/primality_test.hpp
/*!
* Portions corresponding to AtCoder Library (CC0-1.0): Miller-Rabin termination logic.
* Upstream: atcoder/internal_math.hpp
* https://github.com/atcoder/ac-library/tree/864245a00b00dd008d1abfdc239618fdb7d139da
* License: https://github.com/atcoder/ac-library/blob/864245a00b00dd008d1abfdc239618fdb7d139da/LICENSE
*/
namespace internal
{
template <class mint, class Array>
bool is_prime_impl(ll n, const Array &bases)
{
if (n <= 1)
return false;
if (n == 2 || n == 7 || n == 61)
return true;
if (n % 2 == 0)
return false;
ll d = (n - 1) >> countr_zero(n - 1);
mint::set_mod(n);
for (ll a : bases)
{
ll t = d;
mint y = mint(a).pow(t);
while (t != n - 1 && y != 1 && y != n - 1)
{
y *= y;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0)
return false;
}
return true;
}
};
bool is_prime(ll n)
{
static constexpr array<ll, 3> bases32 = {2, 7, 61};
static constexpr array<ll, 7> bases64 = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
if (n <= INT_MAX)
{
using mint = dynamic_modint32<INT_MIN>;
return internal::is_prime_impl<mint>(n, bases32);
}
else
{
using mint = dynamic_modint64_odd<INT_MIN>;
return internal::is_prime_impl<mint>(n, bases64);
}
}
// https://github.com/miscalculation53/library/tree/wip/math/prime/large/factorize.hpp
namespace internal
{
template <class mint>
ll get_prime_factor_impl(ll n)
{
mint::set_mod(n);
int m = pow(n, .125);
while (true)
{
int c = randrange(1, 100);
mint x = 2, y = 2, prod = 1;
ll g = 1;
while (g == 1)
{
repi(i, m)
{
x = x * x + c;
y = y * y + c, y = y * y + c;
prod *= x - y;
}
g = gcd(prod.val(), n);
}
if (g == n)
continue;
if (is_prime(g))
return g;
else if (is_prime(n / g))
return n / g;
else
return get_prime_factor_impl<mint>(g);
}
}
ll get_prime_factor(ll n)
{
if (n <= INT_MAX)
{
using mint = dynamic_modint32<INT_MIN>;
return get_prime_factor_impl<mint>(n);
}
else
{
using mint = dynamic_modint64_odd<INT_MIN>;
return get_prime_factor_impl<mint>(n);
}
}
};
vc<PrimePower<ll>> factorize(ll n)
{
vc<PrimePower<ll>> res;
repi(p, 2, 100)
{
if (n % p == 0)
{
auto [e, pe, nn] = ord_pow_div(n, p);
res.emplace_back(PrimePower<ll>(p, e, pe));
n = nn;
}
}
while (n > 1)
{
if (is_prime(n))
{
res.emplace_back(n);
break;
}
ll p = internal::get_prime_factor(n);
auto [e, pe, nn] = ord_pow_div(n, p);
res.emplace_back(PrimePower<ll>(p, e, pe));
n = nn;
}
sort(ALL(res), [&](const PrimePower<ll> &pp1, const PrimePower<ll> &pp2)
{ return pp1.p < pp2.p; });
return res;
}
// https://github.com/miscalculation53/library/tree/wip/math/prime/large/euler_phi_carmichael.hpp
//! https://37zigen.com/primitive-root/#i-4
//! https://x.com/noshi91/status/1317025404700405760
namespace internal
{
template <class mint, class I>
vc<mint> lagrange_basis(const vc<I> &a, mint x)
{
const int n = a.size();
vc<mint> res(n);
if (n == 0)
return res;
auto dfs = [&](auto dfs, mint v, int l, int r)
{
if (r - l == 1)
{
res[l] = v;
return;
}
int m = (l + r) / 2;
mint v_l = v, v_r = v;
repi(i, l, m) v_r = v_r.pow(a[i]);
repi(i, m, r) v_l = v_l.pow(a[i]);
dfs(dfs, v_l, l, m);
dfs(dfs, v_r, m, r);
};
dfs(dfs, x, 0, n);
return res;
}
template <class mint, class P>
bool internal_is_primitive_root(ll x, ll p, const vc<PrimePower<P>> &fac)
{
const int k = fac.size();
mint::set_mod(p);
vc<ll> a(k);
repi(i, k) a[i] = fac[i].pe;
auto b = lagrange_basis(a, mint(x));
repi(i, k)
{
if (b[i].pow(fac[i].pe / fac[i].p) == 1)
return false;
}
return true;
}
template <class mint, class P>
ll internal_primitive_root(ll p, const vc<PrimePower<P>> &fac)
{
if (p == 2)
return 1;
while (true)
{
ll g = randrange(1, p);
if (internal_is_primitive_root<mint>(g, p, fac))
return g;
}
}
};
template <class P>
ll primitive_root(ll p, const vc<PrimePower<P>> &fac)
{
if (p <= INT_MAX)
{
using mint = dynamic_modint32<INT_MIN>;
return internal::internal_primitive_root<mint>(p, fac);
}
else
{
using mint = dynamic_modint64_odd<INT_MIN>;
return internal::internal_primitive_root<mint>(p, fac);
}
}
// https://github.com/miscalculation53/library/tree/wip/ds/dynamic_bitset.hpp
struct DynamicBitset
{
using Word = ull;
static constexpr int word_bits = numeric_limits<Word>::digits;
private:
int n;
vc<Word> dat;
static int word_size(int n) { return (n + word_bits - 1) / word_bits; }
static Word low_mask(int k)
{
return k == word_bits ? ~Word(0) : (Word(1) << k) - 1;
}
Word last_mask() const
{
return n % word_bits == 0 ? ~Word(0) : low_mask(n % word_bits);
}
void trim()
{
if (!dat.empty())
dat.back() &= last_mask();
}
Word get_word(int i) const
{
int w = i / word_bits, b = i % word_bits;
Word x = dat[w] >> b;
if (b && w + 1 < SZ(dat))
x |= dat[w + 1] << (word_bits - b);
return x;
}
template <int op, class F>
DynamicBitset &apply_slice(int l, int r, const DynamicBitset &b, int bl, const F &f)
{
assert(0 <= l && l <= r && r <= n);
assert(0 <= bl && bl <= b.n);
r = l + min(r - l, b.n - bl);
if (l == r)
return *this;
if constexpr (op == 2)
{
if (this == &b && bl == 0 && l > 0)
{
int dw = l / word_bits, db = l % word_bits;
int lw = l / word_bits, rw = (r - 1) / word_bits;
repi(w, rw, lw - 1, -1)
{
Word x = dat[w - dw] << db;
if (db && w > dw)
x |= dat[w - dw - 1] >> (word_bits - db);
int lo = max(l, w * word_bits), hi = min(r, (w + 1) * word_bits);
Word mask = low_mask(hi - lo) << (lo % word_bits);
Word added = x & ~dat[w] & mask;
dat[w] |= x & mask;
if constexpr (!is_same_v<F, nullptr_t>)
{
while (added)
{
f(w * word_bits + __builtin_ctzll(added));
added &= added - 1;
}
}
}
return *this;
}
}
auto apply_word = [&](int w)
{
int lo = max(l, w * word_bits), hi = min(r, (w + 1) * word_bits);
int len = hi - lo, shift = lo % word_bits;
Word mask = low_mask(len) << shift;
Word x = (b.get_word(bl + lo - l) & low_mask(len)) << shift;
Word old = dat[w], y;
if constexpr (op == 0)
y = x;
else if constexpr (op == 1)
y = old & x;
else if constexpr (op == 2)
y = old | x;
else
y = old ^ x;
dat[w] = (old & ~mask) | (y & mask);
if constexpr (!is_same_v<F, nullptr_t>)
{
Word added = dat[w] & ~old & mask;
while (added)
{
f(w * word_bits + __builtin_ctzll(added));
added &= added - 1;
}
}
};
int lw = l / word_bits, rw = (r - 1) / word_bits;
if constexpr (op == 2 && is_same_v<F, nullptr_t>)
{
if (this != &b && lw < rw)
{
apply_word(lw);
apply_word(rw);
int si = bl + (lw + 1) * word_bits - l;
int sw = si / word_bits, sb = si % word_bits;
if (sb == 0)
repi(w, lw + 1, rw) dat[w] |= b.dat[sw++];
else
repi(w, lw + 1, rw)
{
dat[w] |= (b.dat[sw] >> sb) | (b.dat[sw + 1] << (word_bits - sb));
sw++;
}
return *this;
}
}
if (this == &b && bl < l && l < bl + r - l)
repi(w, rw, lw - 1, -1) apply_word(w);
else
repi(w, lw, rw + 1) apply_word(w);
return *this;
}
public:
struct Reference
{
DynamicBitset *bs;
int pos;
operator bool() const { return bs->test(pos); }
Reference &operator=(bool value)
{
bs->set(pos, value);
return *this;
}
Reference &operator=(const Reference &ref) { return *this = bool(ref); }
Reference &flip()
{
bs->flip(pos);
return *this;
}
};
DynamicBitset() : n(0) {}
DynamicBitset(int n, bool value = false) : n(n), dat(n < 0 ? 0 : word_size(n), value ? ~Word(0) : 0)
{
assert(n >= 0);
trim();
}
explicit DynamicBitset(const string &s, char zero = '0', char one = '1') : n(0)
{
assign(s, zero, one);
}
int size() const { return n; }
int word_count() const { return dat.size(); }
Word word(int i) const { assert(0 <= i && i < word_count()); return dat[i]; }
DynamicBitset &set_word(int i, Word value)
{
assert(0 <= i && i < word_count());
dat[i] = value;
if (i + 1 == word_count()) trim();
return *this;
}
bool empty() const { return n == 0; }
int capacity() const { return int(dat.capacity()) * word_bits; }
void reserve(int n)
{
assert(n >= 0);
dat.reserve(word_size(n));
}
void resize(int n, bool value = false)
{
assert(n >= 0);
int old = this->n;
dat.resize(word_size(n));
this->n = n;
if (value && old < n)
set_range(old, n);
trim();
}
DynamicBitset &assign(const string &s, char zero = '0', char one = '1')
{
assert(zero != one);
n = int(s.size());
dat.assign(word_size(n), 0);
repi(i, n)
{
char c = s[n - 1 - i];
assert(c == zero || c == one);
if (c == one)
dat[i / word_bits] |= Word(1) << (i % word_bits);
}
return *this;
}
bool test(int i) const
{
assert(0 <= i && i < n);
return dat[i / word_bits] >> (i % word_bits) & 1;
}
bool operator[](int i) const { return test(i); }
Reference operator[](int i)
{
assert(0 <= i && i < n);
return {this, i};
}
DynamicBitset &set(int i, bool value = true)
{
assert(0 <= i && i < n);
Word mask = Word(1) << (i % word_bits);
if (value)
dat[i / word_bits] |= mask;
else
dat[i / word_bits] &= ~mask;
return *this;
}
DynamicBitset &reset(int i) { return set(i, false); }
DynamicBitset &flip(int i)
{
assert(0 <= i && i < n);
dat[i / word_bits] ^= Word(1) << (i % word_bits);
return *this;
}
DynamicBitset &set()
{
fill(ALL(dat), ~Word(0));
trim();
return *this;
}
DynamicBitset &reset()
{
fill(ALL(dat), 0);
return *this;
}
DynamicBitset &flip()
{
fem(x : dat) x = ~x;
trim();
return *this;
}
DynamicBitset &set_range(int l, int r, bool value = true)
{
assert(0 <= l && l <= r && r <= n);
if (!value)
return reset_range(l, r);
if (l == r)
return *this;
int lw = l / word_bits, rw = (r - 1) / word_bits;
if (lw == rw)
dat[lw] |= low_mask((r - 1) % word_bits + 1) & ~low_mask(l % word_bits);
else
{
dat[lw] |= ~low_mask(l % word_bits);
fill(dat.begin() + lw + 1, dat.begin() + rw, ~Word(0));
dat[rw] |= low_mask((r - 1) % word_bits + 1);
}
trim();
return *this;
}
DynamicBitset &reset_range(int l, int r)
{
assert(0 <= l && l <= r && r <= n);
if (l == r)
return *this;
int lw = l / word_bits, rw = (r - 1) / word_bits;
if (lw == rw)
dat[lw] &= ~(low_mask((r - 1) % word_bits + 1) & ~low_mask(l % word_bits));
else
{
dat[lw] &= low_mask(l % word_bits);
fill(dat.begin() + lw + 1, dat.begin() + rw, 0);
dat[rw] &= ~low_mask((r - 1) % word_bits + 1);
}
return *this;
}
DynamicBitset &flip_range(int l, int r)
{
assert(0 <= l && l <= r && r <= n);
if (l == r)
return *this;
int lw = l / word_bits, rw = (r - 1) / word_bits;
if (lw == rw)
dat[lw] ^= low_mask((r - 1) % word_bits + 1) & ~low_mask(l % word_bits);
else
{
dat[lw] ^= ~low_mask(l % word_bits);
repi(w, lw + 1, rw) dat[w] = ~dat[w];
dat[rw] ^= low_mask((r - 1) % word_bits + 1);
}
trim();
return *this;
}
int count() const
{
int res = 0;
fec(x : dat) res += __builtin_popcountll(x);
return res;
}
int count(int l, int r) const
{
assert(0 <= l && l <= r && r <= n);
if (l == r)
return 0;
int lw = l / word_bits, rw = (r - 1) / word_bits;
if (lw == rw)
return __builtin_popcountll(dat[lw] & low_mask((r - 1) % word_bits + 1) & ~low_mask(l % word_bits));
int res = __builtin_popcountll(dat[lw] & ~low_mask(l % word_bits));
repi(w, lw + 1, rw) res += __builtin_popcountll(dat[w]);
return res + __builtin_popcountll(dat[rw] & low_mask((r - 1) % word_bits + 1));
}
bool any() const
{
fec(x : dat) if (x) return true;
return false;
}
bool any(int l, int r) const { return count(l, r) != 0; }
bool none() const { return !any(); }
bool none(int l, int r) const { return !any(l, r); }
bool all() const { return count() == n; }
bool all(int l, int r) const { return count(l, r) == r - l; }
int find_first(bool value = true) const { return find_next(-1, value); }
int find_next(int i, bool value = true) const
{
assert(-1 <= i && i < n);
i++;
if (i == n)
return n;
int w = i / word_bits, b = i % word_bits;
Word x = (value ? dat[w] : ~dat[w]) & (~Word(0) << b);
while (true)
{
if (x)
{
int res = w * word_bits + __builtin_ctzll(x);
return min(res, n);
}
if (++w == SZ(dat))
return n;
x = value ? dat[w] : ~dat[w];
}
}
int find_last(bool value = true) const { return find_prev(n, value); }
int find_prev(int i, bool value = true) const
{
assert(0 <= i && i <= n);
if (i == 0)
return -1;
i--;
int w = i / word_bits, b = i % word_bits;
Word x = (value ? dat[w] : ~dat[w]) & low_mask(b + 1);
while (true)
{
if (x)
return w * word_bits + 63 - __builtin_clzll(x);
if (w-- == 0)
return -1;
x = value ? dat[w] : ~dat[w];
}
}
DynamicBitset &operator&=(const DynamicBitset &b)
{
assert(n == b.n);
repi(i, SZ(dat)) dat[i] &= b.dat[i];
return *this;
}
DynamicBitset &operator|=(const DynamicBitset &b)
{
assert(n == b.n);
repi(i, SZ(dat)) dat[i] |= b.dat[i];
return *this;
}
DynamicBitset &operator^=(const DynamicBitset &b)
{
assert(n == b.n);
repi(i, SZ(dat)) dat[i] ^= b.dat[i];
return *this;
}
friend DynamicBitset operator&(DynamicBitset a, const DynamicBitset &b) { return a &= b; }
friend DynamicBitset operator|(DynamicBitset a, const DynamicBitset &b) { return a |= b; }
friend DynamicBitset operator^(DynamicBitset a, const DynamicBitset &b) { return a ^= b; }
DynamicBitset operator~() const { return DynamicBitset(*this).flip(); }
DynamicBitset &operator<<=(int k)
{
assert(k >= 0);
if (k >= n)
return reset();
if (k == 0)
return *this;
int dw = k / word_bits, db = k % word_bits;
repi(i, SZ(dat) - 1, dw - 1, -1)
{
Word x = dat[i - dw] << db;
if (db && i > dw)
x |= dat[i - dw - 1] >> (word_bits - db);
dat[i] = x;
}
fill(dat.begin(), dat.begin() + dw, 0);
trim();
return *this;
}
DynamicBitset &operator>>=(int k)
{
assert(k >= 0);
if (k >= n)
return reset();
if (k == 0)
return *this;
int dw = k / word_bits, db = k % word_bits, m = SZ(dat);
repi(i, m - dw)
{
Word x = dat[i + dw] >> db;
if (db && i + dw + 1 < m)
x |= dat[i + dw + 1] << (word_bits - db);
dat[i] = x;
}
fill(dat.end() - dw, dat.end(), 0);
trim();
return *this;
}
DynamicBitset operator<<(int k) const { return DynamicBitset(*this) <<= k; }
DynamicBitset operator>>(int k) const { return DynamicBitset(*this) >>= k; }
DynamicBitset rotated_left(int k) const
{
if (n == 0)
return {};
k %= n;
if (k < 0) k += n;
if (k == 0)
return *this;
DynamicBitset res(n);
int p = n - k;
repi(i, SZ(dat))
{
Word x = get_word(p);
const int tail = n - p;
if (tail < word_bits)
x |= dat[0] << tail;
res.dat[i] = x;
p += word_bits;
if (p >= n) p -= n;
}
res.trim();
return res;
}
DynamicBitset rotated_right(int k) const
{
return rotated_left(n == 0 ? 0 : -(k % n));
}
DynamicBitset &rotate_left(int k)
{
if (n != 0 && k % n != 0)
*this = rotated_left(k);
return *this;
}
DynamicBitset &rotate_right(int k)
{
return rotate_left(n == 0 ? 0 : -(k % n));
}
DynamicBitset &assign_slice(int l, int r, const DynamicBitset &b, int bl)
{
return apply_slice<0>(l, r, b, bl, nullptr);
}
DynamicBitset &and_slice(int l, int r, const DynamicBitset &b, int bl)
{
return apply_slice<1>(l, r, b, bl, nullptr);
}
DynamicBitset &or_slice(int l, int r, const DynamicBitset &b, int bl)
{
return apply_slice<2>(l, r, b, bl, nullptr);
}
[[gnu::always_inline]] DynamicBitset &xor_slice(int l, int r, const DynamicBitset &b, int bl)
{
if (l == bl && l % word_bits == 0 && r == n && n == b.n)
{
assert(0 <= l && l <= r);
repi(w, l / word_bits, SZ(dat)) dat[w] ^= b.dat[w];
return *this;
}
return apply_slice<3>(l, r, b, bl, nullptr);
}
void push_back(bool value)
{
int i = n;
resize(n + 1);
if (value)
set(i);
}
void pop_back()
{
assert(n > 0);
resize(n - 1);
}
string to_string(char zero = '0', char one = '1') const
{
assert(zero != one);
string res(n, zero);
repi(i, n) if (test(i)) res[n - 1 - i] = one;
return res;
}
vc<bool> content() const
{
vc<bool> res(n);
repi(i, n) res[i] = test(i);
return res;
}
friend bool operator==(const DynamicBitset &a, const DynamicBitset &b)
{
return a.n == b.n && a.dat == b.dat;
}
friend bool operator!=(const DynamicBitset &a, const DynamicBitset &b) { return !(a == b); }
friend bool operator<(const DynamicBitset &a, const DynamicBitset &b)
{
assert(a.n == b.n);
repi(i, SZ(a.dat) - 1, -1, -1)
if (a.dat[i] != b.dat[i])
return a.dat[i] < b.dat[i];
return false;
}
friend bool operator>(const DynamicBitset &a, const DynamicBitset &b) { return b < a; }
friend bool operator<=(const DynamicBitset &a, const DynamicBitset &b) { return !(b < a); }
friend bool operator>=(const DynamicBitset &a, const DynamicBitset &b) { return !(a < b); }
};
void rd1(DynamicBitset &a)
{
string s;
fastio::rd1(s);
a.assign(s);
}
void wt1(const DynamicBitset &a)
{
fastio::wt1(a.to_string());
}
void main2()
{
const ll P = mint::mod();
const ll g = primitive_root(P, factorize(P - 1));
LL(N, Q);
vc<mint> A(N);
rep(i, N) A[i] = xor128();
dump(A);
vc<mint> pw(P - 1);
pw[0] = 1;
rep(i, 1, P - 1) pw[i] = pw[i - 1] * g;
vl lg(P);
rep(i, P - 1) lg[pw[i].val()] = i;
vl B;
rep(i, N) if (A[i] != 0) B.eb(lg[A[i].val()]);
vl ipw(P);
rep(i, P - 1) ipw[pw[i].val()] = i;
DynamicBitset ok(P - 1), rem(P - 1, 1);
fe(b : B) ok[safemod(-b, P - 1)] = 1;
vl mem(P - 1);
rep(ans, P - 1, -1, -1)
{
ll z = ipw[ans];
// y + b == z
// rem[y] かつ ok[-b] = ok[y - z] なる y について mem[y] = ans とする
auto tmp = ok.rotated_left(z) & rem;
ll y = tmp.find_first();
while (y < SZ(tmp))
{
mem[y] = ans;
rem[y] = 0;
y = tmp.find_next(y);
}
}
rep(_, Q)
{
LL(x);
if (x == 0)
PRINT(0);
else
{
ll y = lg[x];
// ll ans = 0;
// fe(b : B) chmax(ans, pw[(y + b) % (P - 1)].val());
// PRINT(ans);
PRINT(mem[y]);
}
}
}
void test()
{
}
// https://github.com/miscalculation53/library/tree/wip/template/template_main.hpp
template <auto init, auto main2, auto test>
struct Main
{
Main()
{
cauto CERR = [](string val, string color)
{
string s = "\033[" + color + "m" + val + "\033[m";
};
CERR("\n[FAST_IO]\n\n", "32");
cout << fixed << setprecision(20);
init();
CERR("\n[SINGLE_TESTCASE]\n\n", "36");
main2();
}
};
Main<init, main2, test> main_dummy;
int main() {}
// submit-code: hash=e5a57f7f6da2 source=e5a57f7f6da2179a77334a73418a9bc156ec6e5d0e303164f85915b0e6f10a4d input=1135f001ac08a149852e04d806a6c5602013f75cdf7f5495c715c047e84cbb94 body=f8bdc87babce0d8a6524d5e3141440ec8c00421ff285bb3769d53982ebe0a4d0