結果
| 問題 | No.3669 误差绝不允许 |
| コンテスト | |
| ユーザー |
 miscalc
|
| 提出日時 | 2026-09-05 20:34:36 |
| 言語 | C++23 (gcc 15.3.0 + boost 1.92.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 65,004 bytes |
| 記録 | |
| コンパイル時間 | 5,468 ms |
| コンパイル使用メモリ | 415,036 KB |
| 実行使用メモリ | 126,644 KB |
| 最終ジャッジ日時 | 2026-09-05 20:34:55 |
| 合計ジャッジ時間 | 14,000 ms |
|
ジャッジサーバーID （参考情報） |
judge3_0 / judge1_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 6 WA * 6 TLE * 1 -- * 17 |
ソースコード
#define SINGLE_TESTCASE
#define FAST_IO
#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;
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 (int i = neg; i < (int)s.size(); i++)
res = 10 * res + 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 = x;
while (ux > 0)
{
res += '0' + ux % 10;
ux /= 10;
}
reverse(res.begin(), res.end());
return sign + res;
}
istream &operator>>(istream &is, i128 &a)
{
string s;
is >> s;
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 rep1(i,n) for (ll i = 0, nnnnn = ll(n); i < nnnnn; i++)
#define rep2(i,l,r) for (ll i = ll(l), rrrrr = ll(r); i < rrrrr; i++)
#define rep3(i,l,r,d) for (ll i = ll(l), rrrrr = ll(r), ddddd = ll(d); ddddd > 0 ? i < rrrrr : i > rrrrr; i += d)
#define rep(...) overload4(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__)
#define repi1(i,n) for (int i = 0, nnnnn = int(n); i < nnnnn; i++)
#define repi2(i,l,r) for (int i = int(l), rrrrr = int(r); i < rrrrr; i++)
#define repi3(i,l,r,d) for (int i = int(l), rrrrr = int(r), ddddd = int(d); ddddd > 0 ? i < rrrrr : i > rrrrr; i += 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>;
template <class T, class U>
inline bool chmin(T &a, U b) { return a > b ? a = b, true : false; }
template <class T, class U>
inline bool chmax(T &a, U b) { return a < b ? a = b, true : false; }
template <class T = ll, class U, class V, typename = enable_if_t<is_integral_ext<U> && is_integral_ext<V>>>
inline constexpr T divfloor(U a, V b) { return T(a) / T(b) - (T(a) % T(b) && (T(a) ^ T(b)) < 0); }
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) { return T(a) - T(b) * divfloor<T>(a, b); }
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://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) ([&](auto x) { return fx; })
#define GEN_VEC(n,i,fi) (gen_vec(n, LMD(i, fi)))
// https://github.com/miscalculation53/library/tree/wip/template/template_algo.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)>, long> = 0>
const T &resolved_value()
{
static const T value = T(x());
return value;
}
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 = INF>
struct MonoidMin
{
using S = T;
};
template <class T, auto infty = INF>
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
{
};
}
template <class M>
vc<typename M::S> cuml(const vc<typename M::S> &v, int left_index = 0)
{
const int n = v.size();
vc<typename M::S> res(n + 1);
res[0] = M::e();
repi(i, n) res[i + 1] = M::op(res[i], v[i]);
res.erase(res.begin(), res.begin() + left_index);
return res;
}
template <class T>
vc<T> cumlsum(const vc<T> &v, int left_index = 0)
{ return cuml<MonoidAdd<T>>(v, left_index); }
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
#define CPP_DUMP_DEFINE_DATA(...)
#define dump(...)
#define local(...)
#define oj(...) __VA_ARGS__
#define local_oj(a,b) (b)
namespace fastio {
template <class T>
struct unsigned_integer
{
using type = make_unsigned_t<T>;
};
template <>
struct unsigned_integer<i128>
{
using type = u128;
};
template <>
struct unsigned_integer<u128>
{
using type = u128;
};
template <class T>
using unsigned_integer_t = typename unsigned_integer<T>::type;
static constexpr uint32_t SIZ = 1 << 17;
char ibuf[SIZ];
char obuf[SIZ];
char out[100];
uint32_t pil = 0, pir = 0, por = 0;
struct Pre {
char num[10000][4];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
memcpy(ibuf, ibuf + pil, pir - pil);
pir = pir - pil + fread(ibuf + pir - pil, 1, SIZ - pir + pil, stdin);
pil = 0;
if (pir < SIZ) ibuf[pir++] = '\n';
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
void rd1(char &c) {
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (c <= ' ');
}
void rd1(string &x) {
x.clear();
while (true) {
if (pil == pir) load();
while (pil < pir && ibuf[pil] <= ' ') ++pil;
if (pil < pir) break;
}
while (true) {
uint32_t p = pil;
while (pil < pir && ibuf[pil] > ' ') ++pil;
x.append(ibuf + p, pil - p);
if (pil < pir) {
++pil;
return;
}
load();
}
}
template <typename T>
void rd1_real(T &x) {
string s;
rd1(s);
auto [p, ec] = from_chars(s.data(), s.data() + s.size(), x);
if (ec == errc{} && p == s.data() + s.size()) return;
if constexpr (is_same_v<T, long double>)
x = stold(s);
else
x = stod(s);
}
template <bool check_buffer = true, typename T>
void rd1_integer(T &x) {
using U = unsigned_integer_t<T>;
bool minus = false;
U val = 0;
if constexpr (check_buffer)
if (pil + 100 > pir) load();
uint32_t p = pil;
while (ibuf[p] < '-') ++p;
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (ibuf[p] == '-') minus = true, ++p;
}
while ('0' <= ibuf[p]) val = val * 10 + (ibuf[p++] & 15);
pil = p;
if constexpr (is_signed<T>::value || is_same_v<T, i128>)
{
if (minus)
{
const U min_abs = U(numeric_limits<T>::max()) + 1;
x = val == min_abs ? numeric_limits<T>::lowest() : -T(val);
}
else x = T(val);
}
else
x = T(val);
}
void rd1(int &x) { rd1_integer(x); }
void rd1(ll &x) { rd1_integer(x); }
void rd1(i128 &x) { rd1_integer(x); }
void rd1(uint &x) { rd1_integer(x); }
void rd1(ull &x) { rd1_integer(x); }
void rd1(u128 &x) { rd1_integer(x); }
void rd1(double &x) { rd1_real(x); }
void rd1(long double &x) { rd1_real(x); }
template <class... T>
void rd1(tuple<T...> &tpl) {
apply([](auto &...x) { (rd1(x), ...); }, tpl);
}
template <class T>
void rd1(vc<T> &x) {
for (auto &d: x) rd1(d);
}
template <class... T>
void read(T &...x) {
if constexpr (sizeof...(T) <= SIZ / 100 &&
((!is_same_v<T, char> &&
(is_integral_v<T> || is_same_v<T, i128> || is_same_v<T, u128>)) && ...)) {
if (pil + 100 * sizeof...(T) > pir) load();
(rd1_integer<false>(x), ...);
}
else
(rd1(x), ...);
}
void wt1(const char c) {
if (por == SIZ) flush();
obuf[por++] = c;
}
void wt1(string_view s) {
while (!s.empty()) {
if (por == SIZ) flush();
size_t n = min<size_t>(s.size(), SIZ - por);
memcpy(obuf + por, s.data(), n);
por += n;
s.remove_prefix(n);
}
}
template <typename T>
void wt1_integer(T x) {
if (por > SIZ - 100) flush();
using U = unsigned_integer_t<T>;
U ux;
if constexpr (is_signed<T>::value || is_same_v<T, i128>)
{
if (x < 0)
obuf[por++] = '-', ux = U(0) - U(x);
else
ux = U(x);
}
else
ux = x;
int outi;
for (outi = 96; ux >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[ux % 10000], 4);
ux /= 10000;
}
if (ux >= 1000) {
memcpy(obuf + por, pre.num[ux], 4);
por += 4;
} else if (ux >= 100) {
memcpy(obuf + por, pre.num[ux] + 1, 3);
por += 3;
} else if (ux >= 10) {
int q = (ux * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (ux - q * 10) | '0';
por += 2;
} else
obuf[por++] = ux | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
template <typename T>
void wt1_real(T x) {
auto [p, ec] = to_chars(out, out + sizeof(out), x, chars_format::fixed, 15);
if (ec == errc{}) {
wt1(string_view(out, p));
return;
}
ostringstream oss;
oss << fixed << setprecision(15) << x;
wt1(oss.str());
}
void wt1(int x) { wt1_integer(x); }
template <class T, enable_if_t<is_integral_v<T>, int> = 0>
void wt1(T x);
void wt1(i128 x) { wt1_integer(x); }
void wt1(u128 x) { wt1_integer(x); }
void wt1(double x) { wt1_real(x); }
void wt1(long double x) { wt1_real(x); }
template <class T, class U>
void wt1(const pair<T, U> &val);
template <class... T>
void wt1(const tuple<T...> &tpl);
template <class T, size_t S>
void wt1(const array<T, S> &val);
template <class T>
void wt1(const vector<T> &val);
template <class... T>
void write(T &&...x) {
(wt1(std::forward<T>(x)), ...);
}
template <class... T>
void print(T &&...x) {
if constexpr (sizeof...(T))
{
int i = 0;
((i++ ? wt1(' ') : void(), wt1(std::forward<T>(x))), ...);
}
wt1('\n');
}
}
struct Dummy {
Dummy() { atexit(fastio::flush); }
} dummy;
namespace internal
{
template <class... Ts>
void READnodump(Ts &...a) { fastio::read(a...); }
template <class... T>
void READVECnodump(int n, vc<T> &...v)
{
(v.resize(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
{
template <size_t... I, class A, class B>
auto &tuple_add_impl(A &a, const B &b, const index_sequence<I...>)
{
((get<I>(a) += get<I>(b)), ...);
return a;
}
};
template <class... Ts, class Tp>
tuple<Ts...> &operator+=(tuple<Ts...> &a, const Tp &b)
{ return internal::tuple_add_impl(a, b, make_index_sequence<tuple_size_v<tuple<Ts...>>>{}); }
template <class T, class Add>
void offset(vc<T> &v, const Add &add) { for (auto &vi : v) vi += add; }
template <class T, const size_t m>
array<vc<T>, m> unzip(const vc<array<T, m>> &vt)
{
const size_t n = vt.size();
array<vc<T>, m> tv;
tv.fill(vc<T>(n));
for (size_t i = 0; i < n; i++)
for (size_t j = 0; j < m; j++)
tv[j][i] = vt[i][j];
return tv;
}
template <class T, const size_t m>
vc<array<T, m>> zip(const array<vc<T>, m> &tv)
{
if (tv.empty()) return {};
const size_t n = tv[0].size();
vc<array<T, m>> vt(n);
for (size_t j = 0; j < m; j++)
{
assert(tv[j].size() == n);
for (size_t i = 0; i < n; i++)
vt[i][j] = tv[j][i];
}
return vt;
}
template <class T, class U>
pair<vc<T>, vc<U>> unzip(const vc<pair<T, U>> &vt)
{
const size_t n = vt.size();
pair<vc<T>, vc<U>> tv;
tv.first.resize(n), tv.second.resize(n);
for (size_t i = 0; i < n; i++)
tie(tv.first[i], tv.second[i]) = vt[i];
return tv;
}
template <class T, class U>
vc<pair<T, U>> zip(const pair<vc<T>, vc<U>> &tv)
{
const size_t n = tv.first.size();
assert(n == tv.second.size());
vc<pair<T, U>> vt(n);
for (size_t i = 0; i < n; i++)
vt[i] = make_pair(tv.first[i], tv.second[i]);
return vt;
}
namespace internal
{
template <size_t... I, class V, class Tp>
auto vt_to_tv_impl(V &tv, const Tp &t, index_sequence<I...>, size_t index)
{ ((get<I>(tv)[index] = get<I>(t)), ...); }
template <size_t... I, class Tp>
auto tv_to_vt_impl(const Tp &tv, index_sequence<I...>, size_t index)
{ return make_tuple(get<I>(tv)[index]...); }
};
template <class... Ts>
auto unzip(const vc<tuple<Ts...>> &vt)
{
const size_t n = vt.size();
tuple<vc<Ts>...> tv;
apply([&](auto &...v)
{ ((v.resize(n)), ...); }, tv);
for (size_t i = 0; i < n; i++)
internal::vt_to_tv_impl(tv, vt[i], make_index_sequence<tuple_size_v<decltype(tv)>>{}, i);
return tv;
}
template <class... Ts>
auto zip(const tuple<vc<Ts>...> &tv)
{
size_t n = get<0>(tv).size();
apply([&](auto &...v)
{ ((void(v), assert(v.size() == n)), ...); }, tv);
vc<tuple<Ts...>> vt(n);
for (size_t i = 0; i < n; i++)
vt[i] = internal::tv_to_vt_impl(tv, index_sequence_for<Ts...>{}, i);
return vt;
}
#define UNZIP(vt,...) auto [__VA_ARGS__] = unzip(vt)
#define ZIP(vt,...) auto vt = zip(tuple{__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
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_static.hpp
// https://github.com/miscalculation53/library/tree/wip/utils/larger_int.hpp
template <class T>
struct larger_int
{
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>
using larger_int_t = typename larger_int<T>::type;
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_isprime.hpp
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 <class T>
constexpr bool isprime_constexpr(T n)
{
if constexpr (sizeof(T) > 4)
{
if (n <= INT_MAX)
return isprime_constexpr<int>(n);
}
if (n <= 1)
return false;
if (n == 2 || n == 7 || n == 61)
return true;
if (n % 2 == 0)
return false;
ll d = n - 1;
while (d % 2 == 0)
d /= 2;
using U = make_unsigned_t<T>;
using L = larger_int_t<U>;
auto miller_rabin = [&](const auto &bases) constexpr
{
for (ll a : bases)
{
ll t = d, y = powmod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1)
{
y = L(y) * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0)
return false;
}
return true;
};
if constexpr(sizeof(T) <= 4)
{
constexpr ll bases[3] = {2, 7, 61};
return miller_rabin(bases);
}
else
{
constexpr ll bases[7] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
return miller_rabin(bases);
}
}
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 = larger_int_t<value_type>;
static constexpr bool is_prime = isprime_constexpr(M);
static constexpr mod_type mod() { return M; }
static constexpr value_type umod() { 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
namespace internal
{
struct barrett32
{
uint m;
ull im;
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{998244353};
static mod_type mod() { return reducer.umod(); }
static value_type init(value_type v) { return 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, im, sq;
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); }
};
struct montgomery64
{
ull m, mx, imx, d, q;
uint b;
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{(1LL << 61) - 1};
static mod_type mod() { return reducer.umod(); }
static value_type init(value_type v) { return reducer.inv_reduce(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{(1LL << 61) - 1};
static mod_type mod() { return reducer.umod(); }
static value_type init(value_type v) { return reducer.inv_reduce(v); }
};
};
// https://github.com/miscalculation53/library/tree/wip/math/extgcd.hpp
template <class T = ll>
constexpr tuple<T, T, T> extgcd(T a, T b)
{
if (a == 0 && b == 0)
return {0, 0, 0};
T x1 = 1, y1 = 0, z1 = a;
T x2 = 0, y2 = 1, z2 = b;
while (z2 != 0)
{
T q = z1 / z2;
tie(x1, x2) = make_pair(x2, x1 - q * x2);
tie(y1, y2) = make_pair(y2, y1 - q * y2);
tie(z1, z2) = make_pair(z2, z1 - q * z2);
}
if (z1 < 0)
x1 = -x1, y1 = -y1, z1 = -z1;
return {z1, x1, y1};
}
namespace internal
{
template <class Policy>
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() { return Policy::mod(); }
modint_impl() : _v(0) {}
template <class T, typename = enable_if_t<is_integral_ext<T>>>
modint_impl(T v)
{
V rem;
if constexpr (is_signed_ext<T>)
{
using S = make_signed_t<V>;
S x = v % S(Policy::umod());
if (x < 0)
x += Policy::umod();
rem = x;
}
else
rem = V(v % Policy::umod());
_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);
mint x = *this, r = 1;
while (n)
{
if (n & 1)
r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const
{
if constexpr (Policy::is_prime)
{
return pow(mod() - 2);
}
else
{
auto [g, x, y] = extgcd<M>(val(), mod());
assert(g == 1);
return mint(x);
}
}
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>
struct is_modint<internal::modint_impl<Policy>> : 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>
struct is_static_modint<static_modint32<m>> : true_type {};
template <ll m>
struct is_static_modint<static_modint64<m>> : 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:
void reserve(int n);
};
// 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_;
static void reserve(int n);
static T inv(int n)
{
n %= T::mod();
if (n < 0)
n += T::mod();
assert(n != 0);
reserve(n);
return inv_[n];
}
};
// 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
{
struct mint_to_rat_fn
{
};
struct rat_closure : std::ranges::range_adaptor_closure<rat_closure>
{
};
template <typename T>
requires(!std::ranges::range<T> && std::invocable<mint_to_rat_fn, T>)
constexpr rat_closure rat()
{
return rat_closure{};
}
}
using mint = modint998244353;
using bi = Binomial<mint>;
void init()
{
oj(mt.seed(random_device()()));
}
// https://github.com/miscalculation53/library/tree/wip/math/bigint.hpp
// https://github.com/miscalculation53/library/tree/wip/math/convolution/convolution_ll.hpp
// https://github.com/miscalculation53/library/tree/wip/math/convolution/convolution.hpp
// https://github.com/miscalculation53/library/tree/wip/math/crt.hpp
template <class T = ll, class R0, class R1, class M0, class M1>
constexpr tuple<bool, T, T> crt2(R0 r0_, R1 r1_, M0 m0_, M1 m1_)
{
T m0 = m0_, m1 = m1_;
assert(m0 >= 1 && m1 >= 1);
T r0 = safemod(r0_, m0), r1 = safemod(r1_, m1);
if (m0 < m1)
swap(r0, r1), swap(m0, m1);
if (m0 % m1 == 0)
{
if (r0 % m1 != r1)
return {false, 0, 0};
return {true, r0, m0};
}
auto [g, im, _] = extgcd<T>(m0, m1);
T u1 = m1 / g;
if ((r1 - r0) % g)
return {false, 0, 0};
T x = (r1 - r0) / g % u1 * im % u1;
r0 += x * m0;
m0 *= u1;
if (r0 < 0)
r0 += m0;
return {true, r0, m0};
}
template <class T = ll, class V1, class V2>
constexpr tuple<bool, T, T> crt(const V1 &rs, const V2 &ms)
{
assert(rs.size() == ms.size());
const int n = rs.size();
T r = 0, m = 1;
repi(i, n)
{
auto [ok, nr, nm] = crt2<T>(r, rs[i], m, ms[i]);
if (!ok)
return {false, 0, 0};
r = nr, m = nm;
}
return {true, r, m};
}
namespace internal
{
constexpr int primitive_root_constexpr(int m)
{
if (m == 2)
return 1;
if (m == 167772161)
return 3;
if (m == 469762049)
return 3;
if (m == 754974721)
return 11;
if (m == 998244353)
return 3;
if (m == 1107296257)
return 10;
if (m == 1711276033)
return 29;
if (m == 1811939329)
return 13;
if (m == 2013265921)
return 31;
if (m == 2113929217)
return 5;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0)
x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2)
{
if (x % i == 0)
{
divs[cnt++] = i;
while (x % i == 0)
{
x /= i;
}
}
}
if (x > 1)
{
divs[cnt++] = x;
}
for (int g = 2;; g++)
{
bool ok = true;
for (int i = 0; i < cnt; i++)
{
if (powmod_constexpr(g, (m - 1) / divs[i], m) == 1)
{
ok = false;
break;
}
}
if (ok)
return g;
}
}
template <int m>
constexpr int primitive_root_for_convolution = primitive_root_constexpr(m);
template <class mint, int g = internal::primitive_root_for_convolution<mint::mod()>>
struct fft_info
{
static constexpr int rank2 = countr_zero(mint::mod() - 1);
std::array<mint, std::max(3, rank2 + 1)> root;
std::array<mint, std::max(3, rank2 + 1)> iroot;
std::array<mint, std::max(1, rank2 - 2 + 1)> rate2;
std::array<mint, std::max(1, rank2 - 2 + 1)> irate2;
std::array<mint, std::max(1, rank2 - 3 + 1)> rate3;
std::array<mint, std::max(1, rank2 - 3 + 1)> irate3;
fft_info()
{
root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
iroot[rank2] = root[rank2].inv();
for (int i = rank2 - 1; i >= 0; i--)
{
root[i] = root[i + 1] * root[i + 1];
iroot[i] = iroot[i + 1] * iroot[i + 1];
}
{
mint prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 2; i++)
{
rate2[i] = root[i + 2] * prod;
irate2[i] = iroot[i + 2] * iprod;
prod *= iroot[i + 2];
iprod *= root[i + 2];
}
}
{
mint prod = 1, iprod = 1;
for (int i = 0; i <= rank2 - 3; i++)
{
rate3[i] = root[i + 3] * prod;
irate3[i] = iroot[i + 3] * iprod;
prod *= iroot[i + 3];
iprod *= root[i + 3];
}
}
}
};
}
template <class mint>
bool ntt_ok(int n)
{
if (n <= 0)
return false;
if constexpr (is_static_modint_v<mint>)
{
if constexpr (!internal::isprime<mint::mod()>)
return false;
static constexpr int rank2 = countr_zero(mint::mod() - 1);
return n <= (1 << rank2);
}
else
return false;
}
template <int id>
void ntt(vc<dynamic_modint32<id>> &) { assert(false); }
template <auto mod>
void ntt(vc<internal::modint_impl<internal::policy_static<mod>>> &a)
{
using mint = internal::modint_impl<internal::policy_static<mod>>;
int n = int(a.size());
assert(n > 0);
int h = countr_zero((unsigned int)n);
assert(n == (1 << h));
assert(ntt_ok<mint>(n));
static const internal::fft_info<mint> info;
int len = 0;
while (len < h)
{
if (h - len == 1)
{
int p = 1 << (h - len - 1);
mint rot = 1;
for (int s = 0; s < (1 << len); s++)
{
int offset = s << (h - len);
for (int i = 0; i < p; i++)
{
auto l = a[i + offset];
auto r = a[i + offset + p] * rot;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
if (s + 1 != (1 << len))
rot *= info.rate2[countr_zero(~(unsigned int)(s))];
}
len++;
}
else
{
int p = 1 << (h - len - 2);
mint rot = 1, imag = info.root[2];
for (int s = 0; s < (1 << len); s++)
{
mint rot2 = rot * rot;
mint rot3 = rot2 * rot;
int offset = s << (h - len);
for (int i = 0; i < p; i++)
{
auto mod2 = 1ULL * mint::mod() * mint::mod();
auto a0 = 1ULL * a[i + offset].val();
auto a1 = 1ULL * a[i + offset + p].val() * rot.val();
auto a2 = 1ULL * a[i + offset + 2 * p].val() * rot2.val();
auto a3 = 1ULL * a[i + offset + 3 * p].val() * rot3.val();
auto a1na3imag =
1ULL * mint(a1 + mod2 - a3).val() * imag.val();
auto na2 = mod2 - a2;
a[i + offset] = a0 + a2 + a1 + a3;
a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
}
if (s + 1 != (1 << len))
rot *= info.rate3[countr_zero(~(unsigned int)(s))];
}
len += 2;
}
}
}
template <auto mod>
void intt(vc<internal::modint_impl<internal::policy_static<mod>>> &a)
{
using mint = internal::modint_impl<internal::policy_static<mod>>;
int n = int(a.size());
assert(n > 0);
int h = countr_zero((unsigned int)n);
assert(n == (1 << h));
assert(ntt_ok<mint>(n));
static const internal::fft_info<mint> info;
int len = h;
while (len)
{
if (len == 1)
{
int p = 1 << (h - len);
mint irot = 1;
for (int s = 0; s < (1 << (len - 1)); s++)
{
int offset = s << (h - len + 1);
for (int i = 0; i < p; i++)
{
auto l = a[i + offset];
auto r = a[i + offset + p];
a[i + offset] = l + r;
a[i + offset + p] =
((unsigned long long)mint::mod() + l.val() - (uint)r.val()) *
irot.val();
;
}
if (s + 1 != (1 << (len - 1)))
irot *= info.irate2[countr_zero(~(unsigned int)(s))];
}
len--;
}
else
{
int p = 1 << (h - len);
mint irot = 1, iimag = info.iroot[2];
for (int s = 0; s < (1 << (len - 2)); s++)
{
mint irot2 = irot * irot;
mint irot3 = irot2 * irot;
int offset = s << (h - len + 2);
for (int i = 0; i < p; i++)
{
auto a0 = 1ULL * a[i + offset + 0 * p].val();
auto a1 = 1ULL * a[i + offset + 1 * p].val();
auto a2 = 1ULL * a[i + offset + 2 * p].val();
auto a3 = 1ULL * a[i + offset + 3 * p].val();
auto a2na3iimag =
1ULL *
mint((mint::mod() + a2 - a3) * iimag.val()).val();
a[i + offset] = a0 + a1 + a2 + a3;
a[i + offset + 1 * p] =
(a0 + (mint::mod() - a1) + a2na3iimag) * irot.val();
a[i + offset + 2 * p] =
(a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) *
irot2.val();
a[i + offset + 3 * p] =
(a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) *
irot3.val();
}
if (s + 1 != (1 << (len - 2)))
irot *= info.irate3[countr_zero(~(unsigned int)(s))];
}
len -= 2;
}
}
}
namespace internal
{
template <class mint>
vc<mint> convolution_naive(const vc<mint> &a, const vc<mint> &b)
{
const int n = a.size(), m = b.size();
const int cnta = n - count(ALL(a), 0), cntb = m - count(ALL(b), 0);
vc<mint> c(n + m - 1);
if ((ll)m * cnta > (ll)n * cntb)
{
repi(j, m)
{
if (b[j] == 0)
continue;
repi(i, n) c[i + j] += a[i] * b[j];
}
}
else
{
repi(i, n)
{
if (a[i] == 0)
continue;
repi(j, m) c[i + j] += a[i] * b[j];
}
}
return c;
}
template <class mint>
vc<mint> convolution_ntt(vc<mint> a, vc<mint> b)
{
const int n = a.size(), m = b.size();
const int z = bit_ceil(n + m - 1);
if (a == b)
{
a.resize(z);
ntt(a);
repi(i, z) a[i] *= a[i];
}
else
{
a.resize(z), b.resize(z);
ntt(a), ntt(b);
repi(i, z) a[i] *= b[i];
}
intt(a);
mint iz = mint(z).inv();
fem(ai : a) ai *= iz;
a.resize(n + m - 1);
return a;
}
template <size_t j, int mod, class T, size_t k>
void convolution_crt_helper(const vc<T> &a, const vc<T> &b, vc<array<T, k>> &cs)
{
using mint = static_modint32<mod>;
const int n = a.size(), m = b.size();
auto c = convolution_ntt(vc<mint>(ALL(a)), vc<mint>(ALL(b)));
repi(i, n + m - 1) cs[i][j] = c[i].val();
}
template <int ...ms, class T>
vc<T> convolution_crt(const vc<T> &a, const vc<T> &b)
{
const int n = a.size(), m = b.size();
constexpr size_t k = sizeof...(ms);
vc<array<T, k>> cs(n + m - 1);
constexpr array<int, k> ms_arr = {ms...};
[&]<size_t... Is>(index_sequence<Is...>)
{
(convolution_crt_helper<Is, ms_arr[Is], T, k>(a, b, cs), ...);
}(make_index_sequence<k>{});
vc<T> c(n + m - 1);
repi(i, n + m - 1) c[i] = get<1>(crt(cs[i], ms_arr));
return c;
}
}
vc<ll> convolution_4e18(const vc<ll> &a, const vc<ll> &b)
{
if (a.empty() || b.empty())
return {};
const int n = a.size(), m = b.size();
const int cnta = n - count(ALL(a), 0), cntb = m - count(ALL(b), 0);
int z = bit_ceil(n + m - 1);
ll naive_work = min(ll(cnta) * m, ll(cntb) * n);
ll ntt_work = ll(z) * max(1, int(countr_zero((unsigned)z)));
if (naive_work <= 18 * ntt_work)
return internal::convolution_naive(a, b);
return internal::convolution_crt<2013265921, 2113929217>(a, b);
}
// 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 <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 <int base = 10, int digit = 6>
struct BigInteger
{
private:
static constexpr int BASE = ipow(base, digit);
vl vec;
bool is_nega = false;
static char digit_to_char(int x) { return x < 10 ? char('0' + x) : char('A' + x - 10); }
void zero_suppress()
{
while (!vec.empty() && vec.back() == 0)
vec.pop_back();
if (vec.empty())
is_nega = false;
}
void carry(int d = -1)
{
const int n = vec.size();
if (n == 0)
return;
if (d < 0)
d = n - 1;
repi(i, d)
{
vec[i + 1] += vec[i] / BASE;
vec[i] = vec[i] % BASE;
}
for (int i = d; !(0 <= vec[i] && vec[i] < BASE); i++)
{
vec.eb(vec[i] / BASE);
vec[i] = vec[i] % BASE;
}
}
void borrow(int si, int mx)
{
ll bor = 0;
repi(i, si, vec.size())
{
ll val = vec[i] - bor;
if (val < 0)
{
bor = (-val + BASE - 1) / BASE;
vec[i] = val + bor * BASE;
}
else
{
vec[i] = val;
bor = 0;
if (i >= mx)
break;
}
}
if (bor > 0)
{
is_nega ^= 1;
ll car = 1;
repi(i, vec.size())
{
ll val = (BASE - 1) - vec[i] + car;
if (val >= BASE)
vec[i] = val - BASE, car = 1;
else
vec[i] = val, car = 0;
}
}
zero_suppress();
if (vec.empty())
is_nega = false;
}
BigInteger operator<<(size_t k) const;
int cmp(const BigInteger &b) const
{
if (is_nega ^ b.is_nega)
return is_nega ? -1 : 1;
if (vec.size() != b.vec.size())
return ((vec.size() < b.vec.size()) ^ is_nega) ? -1 : 1;
repi(i, SZ(vec) - 1, -1, -1)
{
if (vec[i] != b.vec[i])
return ((vec[i] < b.vec[i]) ^ is_nega) ? -1 : 1;
}
return 0;
}
public:
template <class T, typename = enable_if_t<is_integral_ext<T>>>
BigInteger(T x)
{
using U = make_unsigned_ext_t<T>;
U ux = x;
if constexpr (is_signed_ext<T>)
{
if (x < 0)
is_nega = true, ux = -ux;
else
is_nega = false;
}
else
is_nega = false;
if (ux == 0)
return;
while (ux > 0)
{
vec.eb((ll)(ux % BASE));
ux /= BASE;
}
}
string to_string() const
{
const int n = vec.size();
if (n == 0)
return "0";
string s;
s.reserve(size_t(n) * digit + is_nega);
if (is_nega)
s += '-';
ll x = vec.back();
char buf[digit];
int len = 0;
do
{
buf[len++] = digit_to_char(x % base);
x /= base;
} while (x);
repi(i, len - 1, -1, -1) s += buf[i];
repi(i, SZ(vec) - 2, -1, -1)
{
size_t p = s.size();
s.resize(p + digit);
x = vec[i];
repi(j, digit - 1, -1, -1)
{
s[p + j] = digit_to_char(x % base);
x /= base;
}
}
return s;
}
bool operator<(const BigInteger &b) const { return cmp(b) < 0; }
bool operator==(const BigInteger &b) const { return is_nega == b.is_nega && vec == b.vec; }
bool operator!=(const BigInteger &b) const { return !(*this == b); }
friend auto safe_hash_key(const BigInteger &x) { return tie(x.is_nega, x.vec); }
BigInteger operator-() const
{
BigInteger res(*this);
if (!res.vec.empty())
res.is_nega ^= 1;
return res;
}
BigInteger abs() const;
BigInteger &operator+=(const BigInteger &b)
{
if (b.vec.empty())
return *this;
if (vec.size() < b.vec.size())
vec.resize(b.vec.size());
if (is_nega == b.is_nega)
{
repi(i, b.vec.size()) vec[i] += b.vec[i];
carry();
}
else
{
repi(i, b.vec.size()) vec[i] -= b.vec[i];
borrow(0, SZ(b.vec) - 1);
}
return *this;
}
BigInteger &operator*=(const BigInteger &b)
{
if (this->vec.empty() || b.vec.empty())
{
this->vec.clear();
this->is_nega = false;
return *this;
}
bool neg = is_nega ^ b.is_nega;
if (b.vec.size() == 1)
{
*this *= int(b.vec[0]);
is_nega = neg;
return *this;
}
if (vec.size() == 1)
{
int v = vec[0];
*this = b;
*this *= v;
is_nega = neg;
return *this;
}
vec = convolution_4e18(this->vec, b.vec);
carry();
zero_suppress();
is_nega = neg;
return *this;
}
BigInteger operator+(const BigInteger &b) const { return BigInteger(*this) += b; }
BigInteger operator*(const BigInteger &b) const { return BigInteger(*this) *= b; }
BigInteger inv(int d) const
{
assert(!vec.empty());
BigInteger a(abs()), c, c2;
BigInteger b = binsearch(LMD(m, ((a * m).vec.size() <= a.vec.size())), 0, BASE + 1, false, false).first;
const BigInteger ONE(1), TWO(2);
for (int k = 1;; k = min(2 * k, d))
{
c = a * b;
if (SZ(b.vec) >= d + 1 && SZ(c.vec) == SZ(a.vec) + SZ(b.vec) - 1)
{
c2 = c + a;
if (c2.vec.size() == a.vec.size() + b.vec.size())
{
if (c2 == ONE << (SZ(c2.vec) - 1))
b += 1;
break;
}
}
b *= (TWO << (SZ(a.vec) + SZ(b.vec) - 1)) - c;
if (SZ(b.vec) >= k + 1)
b >>= SZ(b.vec) - k - 1;
}
b >>= 1;
if (is_nega)
b = -b;
return b;
}
template <class T, typename = enable_if_t<is_integral_ext<T>>>
BigInteger &operator*=(T v)
{
if (vec.empty() || v == 0)
{
vec.clear();
is_nega = false;
return *this;
}
bool v_nega = false;
using U = make_unsigned_ext_t<T>;
U uv = v;
if constexpr (is_signed_ext<T>)
{
if (v < 0)
v_nega = true, uv = -uv;
}
is_nega ^= v_nega;
using V = larger_int_t<U>;
V car = 0;
repi(i, SZ(vec))
{
car += (V)vec[i] * uv;
vec[i] = (ll)(car % BASE);
car /= BASE;
}
while (car > 0)
{
vec.eb((ll)(car % BASE));
car /= BASE;
}
return *this;
}
// base**i * coef を加算、ならし O(1) 時間
// base**i * coef を減算、数が常に非負の場合はならし O(1) 時間
};
template <int base, int digit>
void wt1(const BigInteger<base, digit> &a)
{
fastio::wt1(a.to_string());
}
// https://github.com/miscalculation53/library/tree/wip/math/rational.hpp
/**
* @brief 約分しない有理数
* @docs docs/math/rational.md
*/
template <class T, class = void>
struct is_rational_ordered : false_type
{};
template <class T>
struct is_rational_ordered<T, void_t<decltype(declval<const T &>() < declval<const T &>())>> : true_type
{};
template <class T>
inline constexpr bool is_rational_ordered_v = is_rational_ordered<T>::value;
template <class T, class = void>
struct rational_has_mod : false_type
{};
template <class T>
struct rational_has_mod<T, void_t<decltype(declval<T>() % declval<T>())>> : true_type
{};
template <class T>
struct Rational
{
using value_type = T;
T num, den;
private:
void normalize_sign()
{
if constexpr (is_rational_ordered_v<T>)
{
if (den == T(0))
{
assert(num != T(0));
num = num < T(0) ? T(-1) : T(1);
}
else if (den < T(0))
num = -num, den = -den;
}
else
assert(den != T(0));
}
public:
Rational() : num(0), den(1) {}
template <class U, enable_if_t<is_integral_ext<U> && !is_same_v<decay_t<U>, T>, int> = 0>
Rational(U num) : num(num), den(1) {}
Rational(const T &num, const T &den) : num(num), den(den)
{
normalize_sign();
}
bool is_infinite() const { return den == T(0); }
pair<T, T> reduced() const;
Rational operator-() const { return {-num, den}; }
Rational &operator+=(const Rational &rhs)
{
if constexpr (is_rational_ordered_v<T>)
{
if (is_infinite() || rhs.is_infinite())
{
if (is_infinite() && rhs.is_infinite())
assert(num == rhs.num);
else if (rhs.is_infinite())
num = rhs.num, den = rhs.den;
return *this;
}
}
T rhs_num = rhs.num, rhs_den = rhs.den;
num = num * rhs_den + rhs_num * den;
den *= rhs_den;
normalize_sign();
return *this;
}
friend Rational operator+(Rational lhs, const Rational &rhs) { return lhs += rhs; }
friend Rational operator-(Rational lhs, const Rational &rhs) { return lhs -= rhs; }
friend Rational operator*(Rational lhs, const Rational &rhs) { return lhs *= rhs; }
friend Rational operator/(Rational lhs, const Rational &rhs) { return lhs /= rhs; }
friend bool operator==(const Rational &lhs, const Rational &rhs)
{
if (lhs.is_infinite() || rhs.is_infinite())
return lhs.is_infinite() && rhs.is_infinite() && lhs.num == rhs.num;
using C = larger_int_t<T>;
return C(lhs.num) * C(rhs.den) == C(rhs.num) * C(lhs.den);
}
friend bool operator!=(const Rational &lhs, const Rational &rhs) { return !(lhs == rhs); }
friend auto safe_hash_key(const Rational &x)
{
if constexpr (rational_has_mod<T>::value)
return x.reduced();
else
return x.num / x.den;
}
template <class U = T, enable_if_t<is_rational_ordered_v<U>, int> = 0>
friend bool operator<(const Rational &lhs, const Rational &rhs)
{
if (lhs.is_infinite() || rhs.is_infinite())
{
if (lhs.is_infinite() && rhs.is_infinite())
return lhs.num < rhs.num;
if (lhs.is_infinite())
return lhs.num < T(0);
return T(0) < rhs.num;
}
using C = larger_int_t<T>;
return C(lhs.num) * C(rhs.den) < C(rhs.num) * C(lhs.den);
}
template <class U = T, enable_if_t<is_rational_ordered_v<U>, int> = 0>
friend bool operator>(const Rational &lhs, const Rational &rhs) { return rhs < lhs; }
template <class U = T, enable_if_t<is_rational_ordered_v<U>, int> = 0>
friend bool operator<=(const Rational &lhs, const Rational &rhs) { return !(rhs < lhs); }
template <class U = T, enable_if_t<is_rational_ordered_v<U>, int> = 0>
friend bool operator>=(const Rational &lhs, const Rational &rhs) { return !(lhs < rhs); }
friend ostream &operator<<(ostream &os, const Rational &x)
{
auto [num, den] = x.reduced();
return os << num << '/' << den;
}
friend void wt1(const Rational &x)
{
auto [num, den] = x.reduced();
using fastio::wt1;
wt1(num), wt1('/'), wt1(den);
}
};
template <class T>
struct is_rational : false_type
{};
template <class T>
struct is_rational<Rational<T>> : true_type
{};
template <class T>
inline constexpr bool is_rational_v = is_rational<T>::value;
namespace std
{
template <class T>
struct numeric_limits<::Rational<T>> : numeric_limits<T>
{
static constexpr bool is_specialized = numeric_limits<T>::is_specialized;
static constexpr bool has_infinity = ::is_rational_ordered_v<T>;
static constexpr bool is_signed = numeric_limits<T>::is_signed;
static constexpr bool is_integer = false;
static constexpr bool is_exact = numeric_limits<T>::is_exact;
};
} // namespace std
// https://github.com/miscalculation53/library/tree/wip/graph/sssp.hpp
// https://github.com/miscalculation53/library/tree/wip/graph/graph.hpp
// https://github.com/miscalculation53/library/tree/wip/ds/csr.hpp
/**
* @brief CSR
* @docs docs/ds/csr.md
*/
template <class T, bool is_erasable = false>
struct CSR
{
protected:
int n, m;
// i (0 <= i < n) 行目を表すのは elist の [start[i], start[i+1])
// pop_back する場合は [start[i], start[i] + len[i])
vc<int> start;
vc<T> elist;
vc<int> len;
inline int get_last(int i) const
{
if constexpr (is_erasable)
return start[i] + len[i];
else
return start[i + 1];
}
template <class Iter>
struct RowBase
{
using iterator = Iter;
using reference = typename iterator_traits<iterator>::reference;
private:
iterator begi, endi;
public:
RowBase(const iterator &begi, const iterator &endi) : begi(begi), endi(endi) {}
inline iterator begin() const { return begi; }
inline iterator end() const { return endi; }
inline reference operator[](int i) const { return *(begi + i); }
};
using Row = RowBase<typename vc<T>::iterator>;
using ConstRow = RowBase<typename vc<T>::const_iterator>;
public:
CSR() {}
// 各行の要素数を指定し、値初期化された CSR を構築する
CSR(const vc<int> &row_sizes)
: n(row_sizes.size())
{
fec(s : row_sizes) assert(s >= 0);
start = cumlsum(row_sizes);
m = start.back();
elist.resize(m);
if constexpr (is_erasable)
len = row_sizes;
}
// (i, elem) が格納された vector
// vv[i] に elem たちが格納された vector
Row operator[](int i) { return Row(elist.begin() + start[i], elist.begin() + get_last(i)); }
ConstRow operator[](int i) const
{ return ConstRow(elist.begin() + start[i], elist.begin() + get_last(i)); }
// 第 i 行の先頭の、平坦な要素列における添字を返す
int offset(int i) const
{
assert(0 <= i && i <= n);
return start[i];
}
// 各行をソートし、同じ行の重複要素を削除する
};
/**
* @brief グラフクラス
* @docs docs/graph/graph.md
*/
template <class Cost>
struct Edge
{
int from, to;
Cost cost;
int index;
Edge() : from(-1), to(-1), index(-1) {}
Edge(int s, int t, Cost c, int i = -1) : from(s), to(t), cost(c), index(i) {}
bool operator<(const Edge &rhs) const;
// 逆辺を返す (もとの辺は変更しない)
};
template <class Cost>
struct GraphArc
{
int to, index;
Cost cost;
bool operator<(const GraphArc &rhs) const;
};
// コンストラクタ: n, es
template <bool is_directed, class Cost, bool is_erasable = false>
struct Graph
{
using E = Edge<Cost>;
using A = GraphArc<Cost>;
protected:
using GE = conditional_t<is_erasable, E, A>;
int n = 0, m = 0, era = 0;
CSR<GE, is_erasable> g;
vc<int> eid_to_elist_id;
struct OutEdgeIter
{
using iterator_category = input_iterator_tag;
using value_type = E;
using difference_type = ptrdiff_t;
using pointer = const E *;
using reference = const E &;
int from;
typename vc<GE>::const_iterator it;
mutable E e;
};
struct OutEdgeRow
{
const Graph *g;
int from, l, r;
};
template <class F>
void build(F input_edge)
{
vc<int> row_sizes(n);
repi(i, m)
{
auto [u, v, w] = input_edge(i);
assert(0 <= u && u < n && 0 <= v && v < n);
row_sizes[u]++;
if constexpr (!is_directed)
if (u != v) row_sizes[v]++;
}
g = CSR<GE, is_erasable>(row_sizes);
if constexpr (is_erasable)
eid_to_elist_id.assign((is_directed ? 1 : 2) * m, -1);
vc<int> cnt(n);
repi(i, m)
{
auto [u, v, w] = input_edge(i);
int j = cnt[u]++;
int k = g.offset(u) + j;
if constexpr (is_erasable)
g[u][j] = E(u, v, w, i);
else
g[u][j] = A{int(v), i, w};
if constexpr (is_erasable)
{
int id = is_directed ? i : 2 * i + (u <= v);
eid_to_elist_id[id] = k;
}
if constexpr (!is_directed)
{
if (u != v)
{
j = cnt[v]++;
k = g.offset(v) + j;
if constexpr (is_erasable)
g[v][j] = E(v, u, w, i);
else
g[v][j] = A{int(u), i, w};
if constexpr (is_erasable)
eid_to_elist_id[2 * i + (v <= u)] = k;
}
}
}
}
public:
template <class I>
Graph(int n, const vc<tuple<I, I, Cost>> &es) : n(n), m(es.size()), era(0)
{
build(LMD(i, es[i]));
}
// 頂点数
template <class I = ll>
I size() const { return n; }
// 辺数
template <class I = ll>
I num_of_edges() const { return m - era; }
// v から出る辺の集合
auto out_edges(int v) const;
// v から出る辺を from を持たない軽量な形で返す
auto out_arcs(int v) const { return g[v]; }
// v から出る頂点の集合
// すべての辺を返す。辺番号順とは限らない
// 無向グラフの場合、各辺は from <= to を満たす
vc<E> edges() const;
// 隣接リスト
// 隣接行列 (辺の本数を格納)
// 入次数の列
// 出次数の列
private:
};
template <class Cost, bool is_erasable = false>
using GraphDirected = Graph<true, Cost, is_erasable>;
template <class Cost, bool is_erasable = false>
using GraphUndirected = Graph<false, Cost, is_erasable>;
// https://github.com/miscalculation53/library/tree/wip/ds/my_queue.hpp
/**
* @brief 自作 queue
* @docs docs/ds/my_queue.md
*/
template <class T>
struct MyQueue
{
private:
vc<T> d;
int pos = 0;
public:
void reserve(int n);
bool empty() const { return pos == SZ<int>(d); }
void push(const T &t) { d.eb(t); }
T &front() { return d[pos]; }
void pop() { pos++; }
};
/**
* @brief 単一始点最短路問題
* @docs docs/graph/sssp.md
*/
// 参考: https://hitonanode.github.io/cplib-cpp/graph/shortest_path.hpp
// todo:
// - fibonacci heap を用いた dijkstra の高速化
// - SPFA 等
template <bool is_directed, class Cost, auto infty = INF>
struct ShortestPath : Graph<is_directed, Cost>
{
using Graph<is_directed, Cost>::Graph;
using Graph<is_directed, Cost>::size;
using Graph<is_directed, Cost>::num_of_edges;
using Graph<is_directed, Cost>::out_edges;
using Graph<is_directed, Cost>::out_arcs;
using Graph<is_directed, Cost>::edges;
private:
static constexpr decltype(auto) inf() { return resolved_value<Cost, infty>(); }
vc<Cost> dists;
vc<Edge<Cost>> prv;
int source = -1;
bool solved_all = false;
void init_solve(int s, int t)
{
source = s;
solved_all = (t == -1);
}
public:
vc<Cost> bfs(int s, int t = -1)
{
const int n = size();
assert(0 <= s && s < n);
init_solve(s, t);
dists.assign(n, inf());
prv.assign(n, {});
MyQueue<int> que;
dists[s] = 0;
que.push(s);
while (!que.empty())
{
auto v = que.front();
que.pop();
if (v == t)
break;
fe(e : out_arcs(v))
{
if (chmin(dists[e.to], dists[v] + e.cost))
{
prv[e.to] = Edge<Cost>(v, e.to, e.cost, e.index);
que.push(e.to);
}
}
}
return dists;
}
vc<Cost> bfs01(int s, int t = -1)
{
const int n = size();
assert(0 <= s && s < n);
init_solve(s, t);
dists.assign(n, inf());
prv.assign(n, {});
vc<int> cur{int(s)}, nxt;
vc<unsigned char> used(n, false);
dists[s] = 0;
while (!cur.empty() || !nxt.empty())
{
if (cur.empty()) cur.swap(nxt);
int v = cur.back();
cur.pop_back();
if (used[v])
continue;
used[v] = true;
if (v == t)
break;
fe(e : out_arcs(v))
{
if (chmin(dists[e.to], dists[v] + e.cost))
{
prv[e.to] = Edge<Cost>(v, e.to, e.cost, e.index);
if (e.cost == 0)
cur.eb(e.to);
else
nxt.eb(e.to);
}
}
}
return dists;
}
// 0 以上 max_cost 以下の整数重みについて Dial 法で最短路を求める
vc<Cost> dial(int s, int max_cost, int t = -1);
vc<Cost> dijkstra(int s, int t = -1)
{
const int n = size();
assert(0 <= s && s < n);
init_solve(s, t);
dists.assign(n, inf());
prv.assign(n, {});
pql<pair<Cost, int>> pque;
dists[s] = 0;
pque.push({0, s});
while (!pque.empty())
{
auto [d, v] = pque.top();
pque.pop();
if (v == t)
break;
if (dists[v] != d)
continue;
fec(e : out_arcs(v))
{
Cost nd = dists[v] + e.cost;
if (chmin(dists[e.to], nd))
{
prv[e.to] = Edge<Cost>(v, e.to, e.cost, e.index);
pque.push({nd, e.to});
}
}
}
return dists;
}
vc<Cost> dijkstra_dense(int s, int t = -1)
{
const int n = size();
assert(0 <= s && s < n);
init_solve(s, t);
dists.assign(n, inf());
prv.assign(n, {});
vc<bool> ok(n, false);
dists[s] = 0;
repi(_, n)
{
Cost mn = inf();
int v = -1;
repi(u, n) if (!ok[u] && chmin(mn, dists[u])) v = u;
if (v == -1)
break;
if (v == t)
break;
ok[v] = true;
fec(e : out_arcs(v))
{
if (chmin(dists[e.to], dists[v] + e.cost))
prv[e.to] = Edge<Cost>(v, e.to, e.cost, e.index);
}
}
return dists;
}
// 最短のウォークとして求める (いくらでも小さくなるなら -infty)
// O(nm)
vc<Cost> bellman_ford(int s)
{
const int n = size();
assert(0 <= s && s < n);
init_solve(s, -1);
dists.assign(n, inf());
prv.assign(n, {});
dists[s] = 0;
repi(t, 2 * n)
{
repi(v, n)
{
if (dists[v] == inf())
continue;
fec(e : out_arcs(v))
{
Cost nd = dists[v] == -inf() ? -inf() : dists[v] + e.cost;
if (dists[e.to] > nd)
{
prv[e.to] = Edge<Cost>(v, e.to, e.cost, e.index);
if (t == n - 1)
dists[e.to] = -inf();
else
dists[e.to] = nd;
}
}
}
}
return dists;
}
vc<Cost> solve(int s, int t = -1)
{
bool neg = false;
int zcnt = 0;
Cost wplus1 = -inf();
Cost max_cost = 0;
bool wpluscnt_geq2 = false;
repi(v, size()) fec(e : out_arcs(v))
{
if (e.cost < 0)
{
neg = true;
break;
}
chmax(max_cost, e.cost);
}
repi(v, size()) fec(e : out_arcs(v))
{
if (e.cost == 0)
zcnt++;
if (e.cost > 0)
{
if (wplus1 < 0)
wplus1 = e.cost;
else if (wplus1 != e.cost)
{
wpluscnt_geq2 = true;
break;
}
}
}
if (neg)
return bellman_ford(s);
else if (wpluscnt_geq2)
{
const ll n = size(), m = num_of_edges();
if (n * n < (m << 4))
return dijkstra_dense(s, t);
else
{
if constexpr (is_integral_ext<Cost>)
{
const u128 c = u128(max_cost);
const ull lg = max<ull>(1, bit_width(ull(n)) - 1);
if (c < u128(INT_MAX) && u128(n) * c <= u128(m) * lg)
return dial(s, int(c), t);
}
return dijkstra(s, t);
}
}
else
{
if (zcnt == 0)
return bfs(s, t);
else
return bfs01(s, t);
}
}
// solve(s, t) の後に呼ぶ
// prv[v] := s から v への最短パスのひとつで v に行くために使った辺 (なければ from=-1, to=-1, cost=-1)
// (t を指定して打ち切っていた場合、t に到達する最短パスのひとつで使った辺は正しく記録される)
// solve(s, t) の後に呼ぶ
// (sssp の実行で t を指定して打ち切っていても動作する)
// cnt[v] := s から v への最短パスの個数
// (**sssp の実行で t を指定して打ち切っていてはいけない**)
};
void main2()
{
LL(N, M);
VEC(tllll, M, UVAB);
offset(UVAB, tllll{-1, -1, 0, 0});
UNZIP(UVAB, U, V, A, B);
vc<Rational<BigInteger<>>> W(M);
rep(j, M) W[j] = Rational{BigInteger<>{A[j]}, BigInteger<>{B[j]}};
ZIP(UVW, U, V, W);
ShortestPath<false, Rational<BigInteger<>>, []()
{ return Rational{BigInteger{1}, BigInteger{0}}; }>
G(N, UVW);
auto ans = G.solve(0);
rep(i, 1, N) PRINT(ans[i].num, ans[i].den);
}
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";
/* コードテストで確認する際にコメントアウトを外す
cerr << val;
//*/
};
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() {}