結果
| 問題 | No.3166 [Cherry 7th Tune *] 桜の守人 |
| コンテスト | |
| ユーザー |
 miscalc
|
| 提出日時 | 2026-10-28 15:57:38 |
| 言語 | C++23 (gcc 15.3.0 + boost 1.92.0 + ACL) |
| 結果 |
AC
不安定
|
| 実行時間 | 939 ms / 2,000 ms |
| + 438µs | |
| コード長 | 60,180 bytes |
| 記録 | |
| コンパイル時間 | 3,295 ms |
| コンパイル使用メモリ | 370,280 KB |
| 実行使用メモリ | 13,700 KB |
| 最終ジャッジ日時 | 2026-10-28 15:58:07 |
| 合計ジャッジ時間 | 23,136 ms |
|
ジャッジサーバーID （参考情報） |
judge4_0 / judge3_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 26 |
ソースコード
//! https://github.com/philip82148/cpp-dump
// #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>
namespace {
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/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
namespace default_infty_detail
{
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>
const T &custom_value();
template <class T>
inline constexpr bool unsupported = false;
}
template <class T>
constexpr decltype(auto) default_infty()
{
if constexpr (default_infty_detail::has_infty<T>::value)
return default_infty_detail::custom_value<T>();
else if constexpr (is_same_v<T, i128> || is_same_v<T, u128>)
return T(INF) * T(INF);
else if constexpr (is_integral_ext<T> && !is_same_v<T, bool>)
{
if constexpr (sizeof(T) >= sizeof(ll))
return T(INF);
else if constexpr (numeric_limits<T>::digits >= 31)
return (T(1) << 30) - 1;
else
return T(numeric_limits<T>::max() / 2);
}
else if constexpr (numeric_limits<T>::has_infinity)
return numeric_limits<T>::infinity();
else
static_assert(default_infty_detail::unsupported<T>, "No default infinity for this type; specify infty explicitly or define T::infty().");
}
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;
}
//! 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, auto x, enable_if_t<!is_invocable_v<decltype(x)>, int> = 0>
constexpr T resolved_value();
template <class T, auto x, enable_if_t<is_invocable_v<decltype(x)>, long> = 0>
const T &resolved_value();
template <class T, auto x = nullptr>
constexpr decltype(auto) resolved_infty()
{
if constexpr (is_same_v<decltype(x), nullptr_t>)
return default_infty<T>();
else
return resolved_value<T, x>();
}
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;
static constexpr S op(S a, S b) { return a + b; }
static constexpr S e()
{
if constexpr (has_e0_v<S>)
return S::e0();
else
return {};
}
};
template <class T, auto infty = nullptr>
struct MonoidMin
{
using S = T;
static constexpr S op(S a, S b) { return min(a, b); }
static constexpr decltype(auto) e() { return resolved_infty<T, infty>(); }
};
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
{
template <class T>
bool binsearch_adjacent(T a, T b)
{
if (a < b)
return a + 1 == b;
if (b < a)
return b + 1 == a;
return false;
}
};
template <class T = ll, class Judge, class InitOk, class InitNg>
pair<T, T> binsearch(const Judge &judge, InitOk init_ok, InitNg init_ng, bool check_ok = true, bool check_ng = true)
{
T ok(init_ok), ng(init_ng);
if (check_ok)
assert(judge(ok));
if (check_ng)
assert(!judge(ng));
while (!internal::binsearch_adjacent(ok, ng))
{
T mid = (ok & ng) + ((ok ^ ng) >> 1);
(judge(mid) ? ok : ng) = mid;
}
return {ok, ng};
}
template <class T = ll, class Judge, class InitVal>
pair<T, T> expsearch(const Judge &judge, InitVal init_val, bool positive = true)
{
T cur(init_val), step = 1;
const bool cur_ok = judge(cur);
auto advance = [&](T x, T d, bool pos) -> T
{
if (pos)
return x > numeric_limits<T>::max() - d ? numeric_limits<T>::max() : x + d;
else
return x < numeric_limits<T>::lowest() + d ? numeric_limits<T>::lowest() : x - d;
};
T prv = advance(cur, 1, !positive);
if (prv != cur && judge(prv) != cur_ok)
{
if (cur_ok)
return {cur, prv};
else
return {prv, cur};
}
while (true)
{
T nxt = advance(cur, step, positive);
assert(nxt != cur && "the boundary must exist in the searched direction");
if (nxt == cur || judge(nxt) != cur_ok)
{
T ok = cur_ok ? cur : nxt;
T ng = cur_ok ? nxt : cur;
return binsearch<T>(judge, ok, ng, false, false);
}
cur = nxt;
if (step > numeric_limits<T>::max() / 2)
step = numeric_limits<T>::max();
else
step *= 2;
}
}
// 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
/*!
* Portions adapted from https://github.com/sassan-dev/cpp-dump/tree/aabd98dd8a4b5ae3f62cf12387a68a9f6591197e
*
* MIT License
*
* Copyright (c) 2023 Ryota Sasaki
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*/
#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);
template <class T>
void rd1(vc<T> &x)
{
if constexpr (is_same_v<T, bool>)
for (size_t i = 0; i < x.size(); ++i) { bool value; rd1(value); x[i] = value; }
else
for (auto &element : x) rd1(element);
}
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');
}
template <class T, enable_if_t<numeric_limits<T>::is_integer, int> = 0>
__attribute__((always_inline)) inline void wt1(T x);
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 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...); }
template <class... T>
void READVECnodump(int n, vc<T> &...v)
{
(v.resize(size_t(n)), ...);
READnodump(v...);
}
};
#define READ(...) internal::READnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define IN(T,...) 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<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<T> __VA_ARGS__; READVEC(n, __VA_ARGS__)
#define VEC2(T,n,m,...) vvc<T> __VA_ARGS__; READVEC2(n, m, __VA_ARGS__)
#define READJAG(...) internal::READJAGnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define JAG(T,n,...) vvc<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
{
};
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;
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 value_type init(value_type v) { return v; }
static constexpr mod_type val(value_type v);
};
};
// 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 value_type init(value_type v) { return v; }
static mod_type val(value_type v);
};
};
// 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 value_type init(value_type v) { return reducer.inv_reduce(v); }
static mod_type val(value_type v);
};
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); }
static mod_type val(value_type 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:
modint_impl();
template <class T, typename = enable_if_t<is_integral_ext<T>>>
modint_impl(T v);
M val() const;
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_modint<1000000000>;
// using mint = modint;
using bi = Binomial<mint>;
void init()
{
oj(mt.seed(random_device()()));
}
// https://github.com/miscalculation53/library/tree/wip/ds/cumulative_sum/imos.hpp
// https://github.com/miscalculation53/library/tree/wip/algebra/algebra_basic_ops.hpp
// https://github.com/miscalculation53/library/tree/wip/algebra/algebra_base.hpp
template <class S_, auto op_, auto e_>
struct Monoid
{
using S = S_;
static constexpr auto op = op_;
static constexpr auto e = e_;
};
template <class S_, auto op_, auto e_, auto inv_>
struct Group
{
using S = S_;
static constexpr auto op = op_;
static constexpr auto e = e_;
static constexpr auto inv = inv_;
};
template <class S_, auto add_, auto e0_, auto mul_, auto e1_>
struct SemiRing
{
using S = S_;
static constexpr auto add = add_;
static constexpr auto e0 = e0_;
static constexpr auto mul = mul_;
static constexpr auto e1 = e1_;
};
template <class S_, auto add_, auto e0_, auto minus_, auto mul_, auto e1_>
struct Ring
{
using S = S_;
static constexpr auto add = add_;
static constexpr auto e0 = e0_;
static constexpr auto minus = minus_;
static constexpr auto mul = mul_;
static constexpr auto e1 = e1_;
};
template <class S_, auto add_, auto e0_, auto minus_, auto mul_, auto e1_, auto inv_>
struct Field
{
using S = S_;
static constexpr auto add = add_;
static constexpr auto e0 = e0_;
static constexpr auto minus = minus_;
static constexpr auto mul = mul_;
static constexpr auto e1 = e1_;
static constexpr auto inv = inv_;
};
template <class M, class = void>
struct HasInverse : false_type {};
template <class M>
struct HasInverse<M, void_t<decltype(M::inv(declval<const typename M::S &>()))>> : true_type {};
template <class M>
struct OppositeMonoid
{
using S = typename M::S;
static constexpr auto e = M::e;
};
template <class G>
struct OppositeGroup
{
using S = typename G::S;
static constexpr auto e = G::e;
static constexpr auto inv = G::inv;
};
template <class M>
struct NormalAndOppositeMonoid
{
struct S
{
typename M::S normal;
typename M::S opposite;
};
};
template <class G>
struct NormalAndOppositeGroup
{
struct S
{
typename G::S normal;
typename G::S opposite;
};
};
template <class SR>
using MonoidOfSemiRingAdd = Monoid<typename SR::S, SR::add, SR::e0>;
template <class SR>
using MonoidOfSemiRingMul = Monoid<typename SR::S, SR::mul, SR::e1>;
template <class R>
using GroupOfRingAdd = Group<typename R::S, R::add, R::e0, R::minus>;
template <class K>
using GroupOfFieldMul = Group<typename K::S, K::mul, K::e1, K::inv>;
template <class Madd, class Mmul>
struct SemiRingFromMonoidMonoid
{
static_assert(is_same_v<typename Madd::S, typename Mmul::S>, "Madd::S and Mmul::S must be identical");
using S = typename Madd::S;
static constexpr auto add = Madd::op;
static constexpr auto e0 = Madd::e;
static constexpr auto mul = Mmul::op;
static constexpr auto e1 = Mmul::e;
};
template <class Gadd, class Mmul>
struct RingFromGroupMonoid
{
static_assert(is_same_v<typename Gadd::S, typename Mmul::S>, "Gadd::S and Mmul::S must be identical");
using S = typename Gadd::S;
static constexpr auto add = Gadd::op;
static constexpr auto e0 = Gadd::e;
static constexpr auto minus = Gadd::inv;
static constexpr auto mul = Mmul::op;
static constexpr auto e1 = Mmul::e;
};
template <class Gadd, class Gmul>
struct FieldFromGroupGroup
{
static_assert(is_same_v<typename Gadd::S, typename Gmul::S>, "Gadd::S and Gmul::S must be identical");
using S = typename Gadd::S;
static constexpr auto add = Gadd::op;
static constexpr auto e0 = Gadd::e;
static constexpr auto minus = Gadd::inv;
static constexpr auto mul = Gmul::op;
static constexpr auto e1 = Gmul::e;
static constexpr auto inv = Gmul::inv;
};
template <class T, class = void>
struct has_e1 : false_type {};
template <class T>
struct has_e1<T, void_t<decltype(T::e1())>> : true_type {};
template <class T>
inline constexpr bool has_e1_v = has_e1<T>::value;
template <class T>
struct MonoidMul
{
using S = T;
};
template <class T>
struct GroupAddSub
{
using S = T;
};
template <class T>
struct GroupMulDiv
{
using S = T;
};
template <class T, auto infty = nullptr>
using SemiRingMinPlus = SemiRingFromMonoidMonoid<MonoidMin<T, infty>, MonoidAdd<T>>;
template <class T, auto infty = nullptr>
using SemiRingMaxPlus = SemiRingFromMonoidMonoid<MonoidMax<T, infty>, MonoidAdd<T>>;
template <class T>
using RingAddSubMul = RingFromGroupMonoid<GroupAddSub<T>, MonoidMul<T>>;
template <class T>
using FieldAddSubMulDiv = FieldFromGroupGroup<GroupAddSub<T>, GroupMulDiv<T>>;
template <class G>
struct Imos
{
using S = typename G::S;
private:
vc<S> d;
public:
};
// https://github.com/miscalculation53/library/tree/wip/ds/segtree/sparse_lazy_segtree.hpp
/*! SPDX-License-Identifier: CC0-1.0
* The interval-splitting updates are independently designed from the tree invariants.
*/
// https://github.com/miscalculation53/library/tree/wip/ds/internal_dump_content.hpp
template <class AM>
struct SparseLazySegmentTree
{
using S = typename AM::S;
using F = typename AM::F;
private:
template <class A, class = void>
struct HasPow : false_type {};
template <class A>
struct HasPow<A, void_t<decltype(A::pow(declval<const S &>(), ll{}))>> : true_type {};
static S repeat(S x, ll len)
{
if constexpr (HasPow<AM>::value)
return AM::pow(x, len);
else
{
S res = AM::e();
while (len)
{
if (len & 1) res = AM::op(res, x);
len >>= 1;
if (len) x = AM::op(x, x);
}
return res;
}
}
struct Entry
{
ll l, r;
S unit, val;
Entry(ll l, ll r, const S &unit) : l(l), r(r), unit(unit), val(repeat(unit, r - l)) {}
};
struct Node
{
Entry entry;
S prod;
F lazy;
ll lo, hi;
array<int, 2> chi;
bool has_lazy;
Node(const Entry &entry)
: entry(entry), prod(entry.val), lazy(AM::id()), lo(entry.l), hi(entry.r), chi{-1, -1}, has_lazy(false) {}
};
ll n;
vc<Node> nodes;
int make_node(const Entry &entry)
{
int i = nodes.size();
nodes.eb(entry);
return i;
}
void all_apply(int i, const F &f)
{
nodes[i].entry.unit = AM::mapping(f, nodes[i].entry.unit);
nodes[i].entry.val = AM::mapping(f, nodes[i].entry.val);
nodes[i].prod = AM::mapping(f, nodes[i].prod);
if (nodes[i].has_lazy)
nodes[i].lazy = AM::composition(f, nodes[i].lazy);
else
{
nodes[i].lazy = f;
nodes[i].has_lazy = true;
}
}
void push(int i)
{
if (!nodes[i].has_lazy) return;
F f = nodes[i].lazy;
repi(d, 2)
{
int j = nodes[i].chi[d];
if (j != -1) all_apply(j, f);
}
nodes[i].lazy = AM::id();
nodes[i].has_lazy = false;
}
void pull(int i)
{
int l = nodes[i].chi[0], r = nodes[i].chi[1];
S sml = l == -1 ? AM::e() : nodes[l].prod;
S smr = r == -1 ? AM::e() : nodes[r].prod;
nodes[i].prod = AM::op(AM::op(sml, nodes[i].entry.val), smr);
nodes[i].lo = l == -1 ? nodes[i].entry.l : nodes[l].lo;
nodes[i].hi = r == -1 ? nodes[i].entry.r : nodes[r].hi;
}
void insert(Entry x, ll a, ll b, int i)
{
push(i);
ll c = a + (b - a) / 2;
int d = x.l < c ? 0 : 1;
if ((d == 0 && nodes[i].entry.l < x.l) || (d == 1 && x.l < nodes[i].entry.l))
swap(x, nodes[i].entry);
int j = nodes[i].chi[d];
if (j == -1)
{
j = make_node(x);
nodes[i].chi[d] = j;
}
else if (d == 0)
insert(std::move(x), a, c, j);
else
insert(std::move(x), c, b, j);
pull(i);
}
void apply_impl(ll l, ll r, const F &f, ll a, ll b, int i, array<optional<Entry>, 2> &cuts)
{
if (nodes[i].hi <= l || r <= nodes[i].lo) return;
if (l <= nodes[i].lo && nodes[i].hi <= r)
{
all_apply(i, f);
return;
}
push(i);
ll lo = nodes[i].lo, hi = nodes[i].hi;
Entry &x = nodes[i].entry;
if (x.l < l && l < x.r)
{
cuts[0].emplace(l, min(r, x.r), AM::mapping(f, x.unit));
if (r < x.r) cuts[1].emplace(r, x.r, x.unit);
x.r = l;
x.val = repeat(x.unit, x.r - x.l);
}
else if (l <= x.l && x.l < r)
{
if (r < x.r)
{
cuts[1].emplace(r, x.r, x.unit);
x.r = r;
x.val = repeat(x.unit, x.r - x.l);
}
x.unit = AM::mapping(f, x.unit);
x.val = AM::mapping(f, x.val);
}
ll c = a + (b - a) / 2;
int li = nodes[i].chi[0], ri = nodes[i].chi[1];
if (li != -1) apply_impl(l, r, f, a, c, li, cuts);
if (ri != -1) apply_impl(l, r, f, c, b, ri, cuts);
pull(i);
for (auto &cut : cuts)
if (cut && max(a, lo) <= cut->l && cut->l < min(b, hi))
{
insert(std::move(*cut), a, b, i);
cut.reset();
}
}
public:
SparseLazySegmentTree(ll n, const S &initial_value) : n(n)
{
assert(n >= 0);
nodes.eb(Entry(0, n, initial_value));
}
void apply(ll l, ll r, const F &f)
{
assert(0 <= l && l <= r && r <= n);
if (l == r) return;
array<optional<Entry>, 2> cuts;
apply_impl(l, r, f, 0, n, 0, cuts);
}
S all_prod() const { return nodes[0].prod; }
};
// https://github.com/miscalculation53/library/tree/wip/algebra/acted_monoid/add_min.hpp
//! SPDX-License-Identifier: CC0-1.0
// https://github.com/miscalculation53/library/tree/wip/algebra/min_max_sum.hpp
template <class T, class L = ll>
struct MonoidLenSum
{
using UL = make_unsigned_ext_t<common_type_t<L, ull>>;
struct S
{
L len;
T val;
CPP_DUMP_DEFINE_DATA(len, val);
};
};
template <class T, auto infty = nullptr>
struct MonoidMinMax
{
struct S
{
T mn = resolved_infty<T, infty>(), mx = -resolved_infty<T, infty>();
CPP_DUMP_DEFINE_DATA(mn, mx);
};
};
template <class T, auto infty = nullptr, class L = ll>
struct MonoidMinSum
{
using UL = make_unsigned_ext_t<common_type_t<L, ull>>;
struct S
{
T mn = resolved_infty<T, infty>(), sum = T{};
L len = 0;
CPP_DUMP_DEFINE_DATA(mn, sum, len);
};
};
template <class T, auto infty = nullptr, class L = ll>
struct MonoidMaxSum
{
using UL = make_unsigned_ext_t<common_type_t<L, ull>>;
struct S
{
T mx = -resolved_infty<T, infty>(), sum = T{};
L len = 0;
CPP_DUMP_DEFINE_DATA(mx, sum, len);
};
};
template <class T, auto infty = nullptr, class L = ll>
struct MonoidMinMaxSum
{
using UL = make_unsigned_ext_t<common_type_t<L, ull>>;
struct S
{
T mn = resolved_infty<T, infty>(), mx = -resolved_infty<T, infty>(), sum = T{};
L len = 0;
CPP_DUMP_DEFINE_DATA(mn, mx, sum, len);
};
};
template <class T, auto infty = nullptr>
struct ActedMonoidAddMin
{
using M = MonoidMin<T, infty>;
using MF = MonoidAdd<T>;
using S = typename M::S;
using F = typename MF::S;
static constexpr auto op = M::op;
static constexpr auto e = M::e;
static constexpr S pow(const S &x, ll k)
{
assert(k >= 0);
return k == 0 ? e() : x;
}
static constexpr S mapping(F f, S x) { return f + x; }
static constexpr auto composition = MF::op;
static constexpr auto id = MF::e;
};
template <class T, auto infty = nullptr>
struct ActedMonoidAddMax
{
using M = MonoidMax<T, infty>;
using MF = MonoidAdd<T>;
using S = typename M::S;
using F = typename MF::S;
static constexpr auto op = M::op;
static constexpr auto e = M::e;
static constexpr auto composition = MF::op;
static constexpr auto id = MF::e;
};
template <class T, auto infty = nullptr>
struct ActedMonoidAddMinMax
{
using M = MonoidMinMax<T, infty>;
using MF = MonoidAdd<T>;
using S = typename M::S;
using F = typename MF::S;
static constexpr auto op = M::op;
static constexpr auto e = M::e;
static constexpr auto composition = MF::op;
static constexpr auto id = MF::e;
};
void main2()
{
LL(N, L, K);
VEC(ll, N, X);
auto judge = [&](ll P)
{
if (P < 0)
return false;
dump(P);
SparseLazySegmentTree<ActedMonoidAddMin<ll>> seg(L, 0);
fe(x : X)
{
ll l = x - P, r = x + P;
if (l < 0)
seg.apply(safemod(l, L), L, 1);
seg.apply(max(0LL, l), min(L, r), 1);
if (r > L)
seg.apply(0, r % L, 1);
dump(seg.content());
}
return seg.all_prod() >= K;
};
ll ans = expsearch(judge, 0).first;
PRINT(ans);
}
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[MULTI_TESTCASE]\n\n", "33");
local(while (true))
{
dump("T");
IN(uint, T);
while (T--)
{
dump("new testcase");
main2();
}
}
}
};
Main<init, main2, test> main_dummy;
}
int main() {}
// submit-code: hash=0772ad2b7395 source=0772ad2b73958fcfb94e56a41fcc3dbf17ce171292c6bda089c9551570676df2 input=c331e85e87f1bbcad3f075657599b6ba3e83f267b29a52ffb8614d8c841a295e body=118886c99e606377c4fffa4e31151c781dacb702f891b3a90d60e10684cedef3