結果
| 問題 | No.2996 Floor Sum |
| コンテスト | |
| ユーザー |
👑 |
| 提出日時 | 2026-10-20 06:09:59 |
| 言語 | C++23 (gcc 15.3.0 + boost 1.92.0 + ACL) |
| 結果 |
TLE
不安定
|
| 実行時間 | - |
| コード長 | 16,467 bytes |
| 記録 | |
| コンパイル時間 | 2,475 ms |
| コンパイル使用メモリ | 344,568 KB |
| 実行使用メモリ | 9,860 KB |
| 最終ジャッジ日時 | 2026-10-20 06:10:36 |
| 合計ジャッジ時間 | 16,054 ms |
|
ジャッジサーバーID （参考情報） |
judge2_0 / judge6_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 10 TLE * 2 |
ソースコード
#line 1 "a.cpp"
// https://qandori.github.io/cp-library/
// #include <atcoder/all>
#include <bits/stdc++.h>
using namespace std;
using std::cerr, std::cin, std::cout;
#define vec vector
typedef long double ld;
#if LONG_MAX == 2147483647L
#undef long
#define long long long
#endif
#define uint unsigned int
#define ulong unsigned long
#define overload3(a, b, c, name, ...) name
#define rep3(i, a, b) for (int i = (a); i < (b); i++)
#define rep2(i, n) rep3(i, 0, n)
#define rep1(n) rep2(__i__, n)
#define rep(...) overload3(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__)
#define per3(i, a, b) for (int i = (b) - 1; i >= (a); i--)
#define per2(i, n) per3(i, 0, n)
#define per1(n) per2(__i__, n)
#define per(...) overload3(__VA_ARGS__, per3, per2, per1)(__VA_ARGS__)
#define all(a) a.begin(), a.end()
#define UNIQUE(a) sort(all(a)), a.erase(unique(all(a)), a.end()), a.shrink_to_fit()
#define sz(a) static_cast<int>(a.size())
#ifndef DEBUG
#define cerr \
if (false) cerr
#undef endl
#define endl '\n'
#endif
inline auto operator^=(vector<bool>::reference a, bool b) noexcept {
if (b) a.flip();
return a;
}
inline auto operator&=(vector<bool>::reference a, bool b) noexcept {
if (!b) a = false;
return a;
}
inline auto operator|=(vector<bool>::reference a, bool b) noexcept {
if (b) a = true;
return a;
}
inline ostream &operator<<(ostream &os, __int128_t value) {
ostream::sentry s(os);
if (s) {
__uint128_t tmp = value;
if (value < 0) tmp = -tmp;
char buffer[128];
char *d = std::end(buffer);
do {
--d;
*d = "0123456789"[tmp % 10];
tmp /= 10;
} while (tmp != 0);
if (value < 0) --d, *d = '-';
const int len = std::end(buffer) - d;
if (os.rdbuf()->sputn(d, len) != len) os.setstate(std::ios_base::badbit);
}
return os;
}
template <typename T, typename S>
ostream &operator<<(ostream &os, pair<T, S> a) {
return os << a.first << ' ' << a.second;
};
template <typename T>
ostream &operator<<(ostream &os, vector<T> a) {
const int n = a.size();
rep(i, n) {
os << a[i];
if (i + 1 != n) os << " ";
}
return os;
}
template <typename T, typename S>
istream &operator>>(istream &is, pair<T, S> &a) {
return is >> a.first >> a.second;
}
template <typename T, size_t n>
ostream &operator<<(ostream &os, array<T, n> a) {
rep(i, n) {
os << a[i];
if (i + 1 != n) os << " ";
}
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &a) {
for (T &i : a) is >> i;
return is;
}
template <typename T, typename S>
bool chmin(T &x, S y) {
if ((T)y < x) {
x = (T)y;
return true;
}
return false;
}
template <typename T, typename S>
bool chmax(T &x, S y) {
if (x < (T)y) {
x = (T)y;
return true;
}
return false;
}
template <typename T>
void operator++(vector<T> &a) {
for (T &i : a) ++i;
}
template <typename T>
void operator--(vector<T> &a) {
for (T &i : a) --i;
}
template <typename T>
void operator++(vector<T> &a, int) {
for (T &i : a) i++;
}
template <typename T>
void operator--(vector<T> &a, int) {
for (T &i : a) i--;
}
void init(), solve();
int main() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(20);
cerr << fixed << setprecision(20);
init();
int t = 1;
cin >> t;
while (t--) solve();
}
// #define COMB_MAX 3e5 + 2022
// #include "lib/math/comb.hpp"
// #include "lib/math/fps.hpp"
#line 1 "lib/math/mint.hpp"
#line 6 "lib/math/mint.hpp"
#include <type_traits>
#if defined(__GNUC__) && !defined(__clang__) && (defined(__x86_64__) || defined(__i386__))
#pragma GCC push_options
#pragma GCC optimize("O3")
#endif
namespace fps_detail {
template <class I>
constexpr bool mint_integral = std::is_integral_v<I>
#if defined(__SIZEOF_INT128__)
|| std::is_same_v<I, __int128> || std::is_same_v<I, unsigned __int128>
#endif
;
struct Mint {
using mint = Mint;
unsigned v = 0;
static constexpr unsigned mod() { return 998244353; }
static unsigned reduce(unsigned long long x) {
return (x + (unsigned long long)(unsigned(x) * 998244351u) * mod()) >> 32;
}
[[gnu::always_inline]] Mint() = default;
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
Mint(I x) {
long long r = x % (long long)mod();
if (r < 0) r += mod();
v = reduce((unsigned long long)r * 932051910);
}
static Mint raw(unsigned x) {
Mint a;
a.v = reduce((unsigned long long)x * 932051910);
return a;
}
static Mint word(unsigned x) {
Mint a;
a.v = x;
return a;
}
unsigned val() const {
unsigned r = reduce(v);
return r < mod() ? r : r - mod();
}
friend std::istream &operator>>(std::istream &is, Mint &x) {
long long value;
if (is >> value) x = Mint(value);
return is;
}
friend std::ostream &operator<<(std::ostream &os, const Mint &x) {
return os << x.val();
}
Mint &operator+=(Mint b) {
v += b.v;
if (v >= 2 * mod()) v -= 2 * mod();
return *this;
}
Mint &operator-=(Mint b) {
v -= b.v;
if (v >> 31) v += 2 * mod();
return *this;
}
Mint &operator*=(Mint b) {
v = reduce((unsigned long long)v * b.v);
return *this;
}
Mint &operator/=(Mint b) { return *this *= b.inv(); }
Mint &operator++() { return *this += Mint(1); }
Mint &operator--() { return *this -= Mint(1); }
Mint operator++(int) {
Mint a = *this;
++*this;
return a;
}
Mint operator--(int) {
Mint a = *this;
--*this;
return a;
}
Mint operator+() const { return *this; }
Mint operator-() const { return word(v ? 2 * mod() - v : 0); }
Mint operator+(Mint b) const { return Mint(*this) += b; }
Mint operator-(Mint b) const { return Mint(*this) -= b; }
Mint operator*(Mint b) const { return Mint(*this) *= b; }
Mint operator/(Mint b) const { return Mint(*this) /= b; }
bool operator==(Mint b) const { return (v < mod() ? v : v - mod()) == (b.v < mod() ? b.v : b.v - mod()); }
bool operator!=(Mint b) const { return !(*this == b); }
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
friend Mint operator+(I a, Mint b) { return Mint(a) + b; }
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
friend Mint operator-(I a, Mint b) { return Mint(a) - b; }
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
friend Mint operator*(I a, Mint b) { return Mint(a) * b; }
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
friend Mint operator/(I a, Mint b) { return Mint(a) / b; }
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
friend bool operator==(I a, Mint b) { return Mint(a) == b; }
template <class I, std::enable_if_t<mint_integral<I>, int> = 0>
friend bool operator!=(I a, Mint b) { return Mint(a) != b; }
Mint pow(long long n) const {
assert(n >= 0);
if (!n) return Mint(1);
Mint r(1), a = *this;
for (; n > 1; n >>= 1, a *= a)
if (n & 1) r *= a;
return r * a;
}
[[gnu::noinline]] Mint inv() const {
assert(*this != Mint(0));
Mint a2 = *this * *this, a3 = a2 * *this;
Mint a7 = a3 * a3 * *this;
Mint a31 = a7;
for (int i = 0; i < 2; ++i) a31 *= a31;
a31 *= a3;
Mint r = a7;
for (int i = 0; i < 3; ++i) r *= r;
r *= a3;
r *= r;
for (int j = 0; j < 4; ++j) {
for (int i = 0; i < 5; ++i) r *= r;
r *= a31;
}
for (int i = 0; i < 3; ++i) r *= r;
return r * a7;
}
};
} // namespace fps_detail
using fps_mint = fps_detail::Mint;
using mint = fps_mint;
#if defined(__GNUC__) && !defined(__clang__) && (defined(__x86_64__) || defined(__i386__))
#pragma GCC pop_options
#endif
#line 140 "a.cpp"
void init() {
// init_comb();
}
#line 1 "lib/math/floor_sum/generalized_floor_sum.hpp"
#line 8 "lib/math/floor_sum/generalized_floor_sum.hpp"
namespace generalized_floor_sum_detail {
using U = std::uint64_t;
template <class T>
constexpr bool integer = std::is_integral_v<T> || std::is_same_v<T, __int128_t> || std::is_same_v<T, __uint128_t>;
template <int N, class T>
T divide(T value) {
if constexpr (integer<T>) return value / T(N);
else {
static const T inverse = T(1) / T(N);
return value * inverse;
}
}
template <int D, class T>
using Table = std::array<std::array<T, D + 1>, D + 1>;
template <int D, class T>
struct Coefficients {
std::array<std::array<T, D + 2>, D + 1> sums{};
std::array<std::array<T, D + 2>, D + 2> choose{};
std::array<T, D + 1> denominator{}, inverse{};
Coefficients() {
for (int i = 0; i <= D + 1; ++i) {
choose[i][0] = choose[i][i] = T(1);
for (int j = 1; j < i; ++j) choose[i][j] = choose[i - 1][j - 1] + choose[i - 1][j];
}
T factorial = 1;
for (int p = 0; p <= D; ++p) {
denominator[p] = factorial * T(p + 1);
for (int k = 0; k <= p + 1; ++k) {
T value = factorial * choose[p + 1][k];
for (int j = 0; j < p; ++j)
if (k <= j + 1) value -= factorial / denominator[j] * choose[p + 1][j] * sums[j][k];
sums[p][k] = value;
}
factorial = denominator[p];
if constexpr (!integer<T>) inverse[p] = T(1) / denominator[p];
}
}
T divide(T value, int p) const {
if constexpr (integer<T>) return value / denominator[p];
else return value * inverse[p];
}
};
template <int D, class T>
const Coefficients<D, T> &coefficients() {
static const Coefficients<D, T> value;
return value;
}
template <int D, class T, class A, class B>
[[gnu::always_inline]] inline void translate(Table<D, T> &result, const Coefficients<D, T> &c, A a, B b,
std::array<T, D + 1> &ak, std::array<T, D + 1> &bk) {
if (a != A(0)) {
ak[0] = T(1);
for (int i = 1; i <= D; ++i) ak[i] = ak[i - 1] * T(a);
for (int q = D; q >= 1; --q)
for (int p = 0; p + q <= D; ++p)
for (int j = 0; j < q; ++j) result[p][q] += c.choose[q][j] * ak[q - j] * result[p + q - j][j];
}
if (b != B(0)) {
bk[0] = T(1);
for (int i = 1; i <= D; ++i) bk[i] = bk[i - 1] * T(b);
for (int q = D; q >= 1; --q)
for (int p = 0; p + q <= D; ++p)
for (int j = 0; j < q; ++j) result[p][q] += c.choose[q][j] * bk[q - j] * result[p][j];
}
}
template <int D, class T>
Table<D, T> euclidean(U n, U m, U a, U b) {
Table<D, T> result{};
if (!n) return result;
if (n == 1) {
result[0][0] = T(1);
T value = T(b / m);
for (int q = 1; q <= D; ++q) result[0][q] = result[0][q - 1] * value;
return result;
}
const auto &c = coefficients<D, T>();
std::array<T, D + 1> sums{}, ak{}, bk{}, kp{};
T x = T(n - 1);
for (int p = 0; p <= D; ++p) {
T value = c.sums[p][p + 1];
for (int j = p; j >= 0; --j) value = value * x + c.sums[p][j];
sums[p] = c.divide(value, p);
}
U u = a / m, v = b / m;
a %= m;
b %= m;
if (a) {
__uint128_t z = __uint128_t(a) * (n - 1) + b;
U k = z >> 64 ? U(z / m) : U(z) / m;
if (k) {
auto child = euclidean<D, T>(k, a, m, m - b - 1);
kp[0] = T(1);
for (int j = 1; j <= D; ++j) kp[j] = kp[j - 1] * T(k);
for (int p = 0; p < D; ++p) {
std::array<T, D + 1> inner{};
for (int i = 0; i < D - p; ++i) {
T value = 0;
for (int j = 0; j <= p + 1; ++j) value += c.sums[p][j] * child[i][j];
inner[i] = c.divide(value, p);
}
for (int q = 1; p + q <= D; ++q) {
T value = sums[p] * kp[q];
for (int i = 0; i < q; ++i) value -= c.choose[q][i] * inner[i];
result[p][q] = value;
}
}
}
}
for (int p = 0; p <= D; ++p) result[p][0] = sums[p];
translate<D>(result, c, u, v, ak, bk);
return result;
}
template <class A, class B>
using Signed = std::enable_if_t<std::is_integral_v<A> && std::is_integral_v<B> &&
(std::is_signed_v<A> || std::is_signed_v<B>), int>;
template <class A>
bool negative(A value) {
if constexpr (std::is_signed_v<A>) return value < 0;
else return false;
}
template <class T, class A>
std::pair<U, T> normalize(A value, U m) {
U x = static_cast<U>(value);
if (!negative(value)) return {x % m, T(x / m)};
x = U(0) - x;
U r = x % m, q = x / m + (r != 0);
if constexpr (integer<T>) return {r ? m - r : 0, T(-__int128_t(q))};
else return {r ? m - r : 0, -T(q)};
}
template <class T, bool Full = false>
auto quadratic(U n, U m, U a, U b) {
std::conditional_t<Full, Table<2, T>, std::array<T, 3>> result{};
if (!n) return result;
T count = T(n), s1 = T(n >> 1) * T(n - 1 + (n & 1)), s2 = divide<3>(s1 * (T(2) * count - T(1)));
U u = a / m, v = b / m;
a %= m;
b %= m;
T f = 0, g = 0, h = 0;
if (a) {
__uint128_t z = __uint128_t(a) * (n - 1) + b;
U k = z >> 64 ? U(z / m) : U(z) / m;
if (k) {
auto child = quadratic<T>(k, a, m, m - b - 1);
T height = T(k);
f = T(n - 1) * height - child[0];
g = s1 * height - divide<2>(child[2] + child[0]);
h = T(n - 1) * height * height - child[0] - T(2) * child[1];
}
}
T at = T(u), bt = T(v);
T f0 = f + at * s1 + bt * count;
T f1 = g + at * s2 + bt * s1;
T f2 = h + T(2) * (at * g + bt * f) + at * at * s2 + bt * (T(2) * at * s1 + bt * count);
if constexpr (Full) {
result[0][0] = count;
result[1][0] = s1;
result[2][0] = s2;
result[0][1] = f0;
result[1][1] = f1;
result[0][2] = f2;
} else result = {f0, f1, f2};
return result;
}
template <class T>
T linear(U n, U m, U a, U b) {
T result = 0;
for (;;) {
if (!n) return result;
if (n == 1) return result + T(b / m);
if (a >= m) result += divide<2>(T(n) * T(n - 1)) * T(a / m), a %= m;
if (b >= m) result += T(n) * T(b / m), b %= m;
__uint128_t z = __uint128_t(a) * n + b;
if (z < m) return result;
if (z >> 64) n = z / m, b = z % m;
else {
U value = z;
n = value / m;
b = value % m;
}
std::swap(a, m);
}
}
}
template <int D, class T = __int128_t>
auto generalized_floor_sum_moments(std::uint64_t n, std::uint64_t m, std::uint64_t a, std::uint64_t b) {
static_assert(D >= 0);
assert(m > 0);
if constexpr (D == 0) return generalized_floor_sum_detail::Table<0, T>{std::array<T, 1>{T(n)}};
else if constexpr (D == 1) {
generalized_floor_sum_detail::Table<1, T> result{};
result[0][0] = T(n);
result[1][0] = n ? generalized_floor_sum_detail::divide<2>(T(n) * T(n - 1)) : T(0);
result[0][1] = generalized_floor_sum_detail::linear<T>(n, m, a, b);
return result;
} else if constexpr (D == 2) return generalized_floor_sum_detail::quadratic<T, true>(n, m, a, b);
else return generalized_floor_sum_detail::euclidean<D, T>(n, m, a, b);
}
template <int P, int Q, class T = __int128_t>
T generalized_floor_sum(std::uint64_t n, std::uint64_t m, std::uint64_t a, std::uint64_t b) {
static_assert(P >= 0 && Q >= 0);
assert(m > 0);
if constexpr (Q == 0) {
if (!n) return T(0);
if constexpr (P == 0) return T(n);
else if constexpr (P == 1) return generalized_floor_sum_detail::divide<2>(T(n) * T(n - 1));
else if constexpr (P == 2) return generalized_floor_sum_detail::divide<6>(T(n) * T(n - 1) * (T(2) * T(n) - T(1)));
else {
const auto &c = generalized_floor_sum_detail::coefficients<P, T>();
T value = c.sums[P][P + 1], x = T(n - 1);
for (int j = P; j >= 0; --j) value = value * x + c.sums[P][j];
return c.divide(value, P);
}
} else if constexpr (P == 0 && Q == 1) return generalized_floor_sum_detail::linear<T>(n, m, a, b);
else return generalized_floor_sum_moments<P + Q, T>(n, m, a, b)[P][Q];
}
template <int D, class T = __int128_t, class A, class B, generalized_floor_sum_detail::Signed<A, B> = 0>
auto generalized_floor_sum_moments(std::uint64_t n, std::uint64_t m, A a, B b) {
using namespace generalized_floor_sum_detail;
static_assert(D >= 0);
assert(m > 0);
if (!negative(a) && !negative(b)) return generalized_floor_sum_moments<D, T>(n, m, U(a), U(b));
if constexpr (D == 0) return generalized_floor_sum_moments<0, T>(n, m, U(0), U(0));
else {
if (!n) return Table<D, T>{};
auto [rb, v] = normalize<T>(b, m);
if (n == 1) {
Table<D, T> result{};
result[0][0] = T(1);
for (int q = 1; q <= D; ++q) result[0][q] = result[0][q - 1] * v;
return result;
}
auto [ra, u] = normalize<T>(a, m);
auto result = generalized_floor_sum_moments<D, T>(n, m, ra, rb);
std::array<T, D + 1> ak{}, bk{};
translate<D>(result, coefficients<D, T>(), u, v, ak, bk);
return result;
}
}
template <int P, int Q, class T = __int128_t, class A, class B, generalized_floor_sum_detail::Signed<A, B> = 0>
T generalized_floor_sum(std::uint64_t n, std::uint64_t m, A a, B b) {
using namespace generalized_floor_sum_detail;
static_assert(P >= 0 && Q >= 0);
assert(m > 0);
if constexpr (Q == 0) return generalized_floor_sum<P, Q, T>(n, m, U(0), U(0));
else {
if (!negative(a) && !negative(b)) return generalized_floor_sum<P, Q, T>(n, m, U(a), U(b));
return generalized_floor_sum_moments<P + Q, T>(n, m, a, b)[P][Q];
}
}
#line 144 "a.cpp"
void solve() {
long p, q, n, m, a, b;
cin >> p >> q >> n >> m >> a >> b;
cout << generalized_floor_sum_moments<21, mint>(n + 1, m, a, b)[p][q] << endl;
}