結果
| 問題 | No.2996 Floor Sum |
| コンテスト | |
| ユーザー |
 noya2
|
| 提出日時 | 2025-04-22 21:53:24 |
| 言語 | C++23 (gcc 15.2.0 + boost 1.90.0) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 29,763 bytes |
| 記録 | |
| コンパイル時間 | 5,612 ms |
| コンパイル使用メモリ | 374,176 KB |
| 実行使用メモリ | 9,416 KB |
| 最終ジャッジ日時 | 2026-07-10 04:05:09 |
| 合計ジャッジ時間 | 6,016 ms |
|
ジャッジサーバーID （参考情報） |
judge3_0 / judge2_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 RE * 1 |
| other | AC * 4 RE * 8 |
ソースコード
#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;
#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"
namespace noya2 {
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p){
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
for (auto &x : v) is >> x;
return is;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
template<typename T>
void out(const vector<vector<T>> &vv){
int s = (int)vv.size();
for (int i = 0; i < s; i++) out(vv[i]);
}
struct IoSetup {
IoSetup(){
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetup_noya2;
} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{
const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 = 998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";
void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }
} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"
#line 6 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"
namespace noya2{
unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
if (a == 0 || b == 0) return a + b;
int n = __builtin_ctzll(a); a >>= n;
int m = __builtin_ctzll(b); b >>= m;
while (a != b) {
int mm = __builtin_ctzll(a - b);
bool f = a > b;
unsigned long long c = f ? a : b;
b = f ? b : a;
a = (c - b) >> mm;
}
return a << std::min(n, m);
}
template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }
long long sqrt_fast(long long n) {
if (n <= 0) return 0;
long long x = sqrt(n);
while ((x + 1) * (x + 1) <= n) x++;
while (x * x > n) x--;
return x;
}
template<typename T> T floor_div(const T n, const T d) {
assert(d != 0);
return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}
template<typename T> T ceil_div(const T n, const T d) {
assert(d != 0);
return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}
template<typename T> void uniq(std::vector<T> &v){
std::sort(v.begin(),v.end());
v.erase(unique(v.begin(),v.end()),v.end());
}
template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }
template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }
template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }
} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()
using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;
namespace noya2{
/* ~ (. _________ . /) */
}
using namespace noya2;
#line 2 "c.cpp"
template<template<int p, int q> class func, int i, int j>
void process(auto ...args){
func<i,j>()(args...);
}
template<template<int p, int q> class func, int i, int ...js>
void inner_loop(std::integer_sequence<int, js...>, auto ...args){
(process<func, i, js>(args...), ...);
}
template<template<int p, int q> class func, int ijsumub, int ...is>
void inner_loop_loop(std::integer_sequence<int, is...>, auto ...args){
(inner_loop<func, is>(std::make_integer_sequence<int, ijsumub-is>{}, args...), ...);
}
template<template<int p, int q> class func, int ijsumub>
void process_loop(auto ...args){
inner_loop_loop<func, ijsumub>(std::make_integer_sequence<int, ijsumub>{}, args...);
}
namespace noya2::internal::floor_sum_loop_mod {
/*
for (int p = 0; p <= s; p++) for (int q = 0; q <= s-p; q++){
for (int i = 0; i <= q; i++) for (int j = 0; j <= q-i; j++){
ret[p][q] += fact(q) / (fact(i) * fact(j) * fact(q-i-j)) * pow(aquo, j) * pow(bquo, q-i-j) * rec[p+j][i];
}
}
*/
template<template<int _p, int _q, int _i, int _j> class func, int p, int q, int i, int j>
void inner_process4(auto&& ...args){
func<p,q,i,j>()(args...);
}
template<template<int _p, int _q, int _i, int _j> class func, int p, int q, int i, int ...js>
void inner_loop4(std::integer_sequence<int, js...>, auto&& ...args){
(inner_process4<func, p, q, i, js>(args...), ...);
}
template<template<int _p, int _q, int _i, int _j> class func, int p, int q, int ...is>
void inner_looploop4(std::integer_sequence<int, is...>, auto&& ...args){
(inner_loop4<func, p, q, is>(std::make_integer_sequence<int, q-is+1>{}, args...), ...);
}
template<template<int _p, int _q, int _i, int _j> class func, int p, int ...qs>
void inner_looplooploop4(std::integer_sequence<int, qs...>, auto&& ...args){
(inner_looploop4<func, p, qs>(std::make_integer_sequence<int, qs+1>{}, args...), ...);
}
template<template<int _p, int _q, int _i, int _j> class func, int sumpq, int ...ps>
void inner_looplooplooploop4(std::integer_sequence<int, ps...>, auto&& ...args){
(inner_looplooploop4<func, ps>(std::make_integer_sequence<int, sumpq-ps+1>{}, args...), ...);
}
template<template<int _p, int _q, int _i, int _j> class func, int sumpq>
void process_loop4(auto&& ...args){
inner_looplooplooploop4<func, sumpq>(std::make_integer_sequence<int, sumpq+1>{}, args...);
}
} // namespace noya2::internal::floor_sum_loop_mod
namespace noya2::internal::floor_sum_loop_rec {
/*
for (int p = 0; p <= s; p++) for (int q = 0; q <= s-p; q++){
ret[p][q] += pow(k, q) * power_sum<mint, p>(n);
for (int i = 0; i <= q-1; i++) for (int j = 0; j <= p+1; j++){
ret[p][q] -= binom(q, i) * coef(p, j) * rec[i][j];
}
}
*/
template<template<int _p, int _q, int _i, int _j> class func, int p, int q, int i, int j>
void inner_process4(auto&& ...args){
func<p,q,i,j>()(args...);
}
template<template<int _p, int _q, int _i, int _j> class func, int p, int q, int i, int ...js>
void inner_loop4(std::integer_sequence<int, js...>, auto&& ...args){
(inner_process4<func, p, q, i, js>(args...), ...);
}
template<template<int _p, int _q, int _i, int _j> class func, int p, int q, int jub, int ...is>
void inner_looploop4(std::integer_sequence<int, is...>, auto&& ...args){
(inner_loop4<func, p, q, is>(std::make_integer_sequence<int, jub>{}, args...), ...);
}
template<template<int _p, int _q, int _i, int _j> class func, int p, int ...qs>
void inner_looplooploop4(std::integer_sequence<int, qs...>, auto&& ...args){
(func<p, qs, -1, -1>()(args...), ...);
(inner_looploop4<func, p, qs, p+2>(std::make_integer_sequence<int, qs>{}, args...), ...);
}
template<template<int _p, int _q, int _i, int _j> class func, int sumpq, int ...ps>
void inner_looplooplooploop4(std::integer_sequence<int, ps...>, auto&& ...args){
(inner_looplooploop4<func, ps>(std::make_integer_sequence<int, sumpq-ps+1>{}, args...), ...);
}
template<template<int _p, int _q, int _i, int _j> class func, int sumpq>
void process_loop4(auto&& ...args){
inner_looplooplooploop4<func, sumpq>(std::make_integer_sequence<int, sumpq+1>{}, args...);
}
} // namespace noya2::internal::floor_sum_loop_rec
#line 2 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"
#line 4 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"
#line 2 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"
#line 4 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"
namespace noya2 {
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime_flag = is_prime_constexpr(n);
// {gcd(a, b), a^{-1} mod b}
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u;
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if (m0 < 0) m0 += b / s;
return {s, m0};
}
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;
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 (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root_flag = primitive_root_constexpr(m);
// constexpr long long primitive_root_constexpr(long long m){
// if (m == (1LL << 47) - (1LL << 24) + 1) return 3;
// return primitive_root_constexpr(static_cast<int>(m));
// }
} // namespace noya2
#line 6 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"
namespace noya2{
struct barrett {
unsigned int _m;
unsigned long long im;
explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
unsigned int umod() const { return _m; }
unsigned int mul(unsigned int a, unsigned int b) const {
unsigned long long z = a;
z *= b;
unsigned long long x = (unsigned long long)((__uint128_t(z) * im) >> 64);
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
template <int m>
struct static_modint {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
constexpr static_modint() : _v(0) {}
template<std::signed_integral T>
constexpr static_modint(T v){
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template<std::unsigned_integral T>
constexpr static_modint(T v){
_v = (unsigned int)(v % umod());
}
constexpr unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
constexpr mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
constexpr mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
constexpr mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
constexpr mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
constexpr mint operator+() const { return *this; }
constexpr mint operator-() const { return mint() - *this; }
constexpr mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
constexpr mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend constexpr mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend constexpr mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend constexpr mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend constexpr mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend constexpr bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend constexpr bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
friend std::ostream &operator<<(std::ostream &os, const mint& p) {
return os << p.val();
}
friend std::istream &operator>>(std::istream &is, mint &a) {
long long t; is >> t;
a = mint(t);
return (is);
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = is_prime_flag<m>;
};
template <int id> struct dynamic_modint {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template<std::signed_integral T>
dynamic_modint(T v){
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template<std::unsigned_integral T>
dynamic_modint(T v){
_v = (unsigned int)(v % umod());
}
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = noya2::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
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 std::ostream &operator<<(std::ostream &os, const mint& p) {
return os << p.val();
}
friend std::istream &operator>>(std::istream &is, mint &a) {
long long t; is >> t;
a = mint(t);
return (is);
}
private:
unsigned int _v;
static barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> noya2::barrett dynamic_modint<id>::bt(998244353);
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
template<typename T>
concept Modint = requires (T &a){
T::mod();
a.inv();
a.val();
a.pow(declval<int>());
};
} // namespace noya2
#line 114 "c.cpp"
namespace noya2::internal::floor_sum {
template<int e>
inline long long powint(long long x){
return x * powint<e-1>(x);
}
template<>
inline long long powint<0>(long long){
return 1;
}
template<std::signed_integral T, int e> constexpr long long factint = factint<T, e-1> * e;
template<std::signed_integral T> constexpr long long factint<T, 0> = 1;
template<Modint mint, int e> constexpr mint factmint = e * factmint<mint, e-1>;
template<Modint mint> constexpr mint factmint<mint, 0> = 1;
template<Modint mint, int e> constexpr mint ifactmint = factmint<mint, e>.inv();
template<Modint mint, int n, int r> constexpr mint binommint = factmint<mint, n> * ifactmint<mint, r> * ifactmint<mint, n-r>;
template<Modint mint, int n> constexpr mint invmint = factmint<mint, n-1> * ifactmint<mint, n>;
template<Modint mint, int n, int k> struct bernoulli_sum;
template<Modint mint, int n> constexpr mint bernoulli = -invmint<mint, n+1> * bernoulli_sum<mint, n, n>::value;
template<Modint mint> constexpr mint bernoulli<mint, 0> = 1;
template<Modint mint, int n, int k> struct bernoulli_sum {
static constexpr mint value = binommint<mint, n+1, k-1> * bernoulli<mint, k-1> + bernoulli_sum<mint, n, k-1>::value;
};
template<Modint mint, int n> struct bernoulli_sum<mint, n, 0> {
static constexpr mint value = 0;
};
template<Modint mint, int k, int ...js>
mint inner_power_sum(std::integer_sequence<int, js...>, mint n){
mint ret = 0;
((ret += binommint<mint, k+1, js> * bernoulli<mint, js>, ret *= n), ...);
return ret;
}
// sum[ i in [0, n) ] i^k
template<Modint mint, int k>
mint power_sum(mint n){
return inner_power_sum<mint, k>(std::make_integer_sequence<int, k+1>{}, n) * invmint<mint, k+1>;
}
template<typename T, int k>
void sayar(const std::array<T, k> &a){
vector<T> b(k);
rep(i,k){
b[i] = a[i];
}
out("ar",b);
}
template<Modint mint, int sumpq>
struct floor_sum_pq_info {
using Int = long long;
static constexpr int array_size = (sumpq+1)*(sumpq+2)/2;
template<int i, int j> static constexpr int idx = (i <= sumpq/2 ? i*(sumpq+2)+j : (sumpq-i)*(sumpq+2)+sumpq+1-j);
static constexpr int idx_func(int i, int j){
return (i <= sumpq/2 ? i*(sumpq+2)+j : (sumpq-i)*(sumpq+2)+sumpq+1-j);
}
template<int q, int i, int j> static constexpr mint choose2 = factmint<mint, q> * ifactmint<mint, i> * ifactmint<mint, j> * ifactmint<mint, q-i-j>;
template<int p, int j> static constexpr mint coef = bernoulli<mint, p-j+1> * binommint<mint, p+1, j> * invmint<mint, p+1>;
template<int p> static constexpr mint coef<p, 0> = 0;
template<int p, int q, int i, int j>
struct inner_assign_mod {
void operator()(std::array<mint, array_size> &rec,
std::array<mint, array_size> &ret,
mint aquo, mint bquo){
std::get<idx<p,q>>(ret) += choose2<q, i, j> * aquo.pow(j) * bquo.pow(q-i-j) * std::get<idx<p+j,i>>(rec);
// std::get<idx<p,q>>(ret) += factmint<mint, q> * ifactmint<mint, i> * ifactmint<mint, j> * ifactmint<mint, q-i-j> * aquo.pow(j) * bquo.pow(q-i-j) * std::get<idx<p+j,i>>(rec);
}
};
template<int p, int q, int i, int j>
struct inner_assign_rec {
void operator()(std::array<mint, array_size> &rec,
std::array<mint, array_size> &ret,
mint, mint){
std::get<idx<p,q>>(ret) -= binommint<mint, q, i> * coef<p, j> * std::get<idx<i,j>>(rec);
}
};
template<int p, int q>
struct inner_assign_rec<p, q, -1, -1> {
void operator()(std::array<mint, array_size> &rec,
std::array<mint, array_size> &ret,
mint n, mint k){
std::get<idx<p,q>>(ret) += k.pow(q) * power_sum<mint, p>(n);
}
};
static std::array<mint, array_size> inner_floor_sum_pq(Int n, Int m, Int a, Int b){
if (n <= 0) return {};
Int aquo = floor_div(a, m);
Int arem = a - aquo * m;
Int bquo = floor_div(b, m);
Int brem = b - bquo * m;
if (aquo != 0 || bquo != 0){
auto rec = inner_floor_sum_pq(n, m, arem, brem);
std::array<mint, array_size> ret = {};
floor_sum_loop_mod::process_loop4<inner_assign_mod, sumpq>(rec, ret, aquo, bquo);
return ret;
}
Int k = floor_div(a * (n - 1) + b, m);
auto rec = inner_floor_sum_pq(k, a, m, m - b + a - 1);
std::array<mint, array_size> ret = {};
floor_sum_loop_rec::process_loop4<inner_assign_rec, sumpq>(rec, ret, n, k);
return ret;
}
};
template<typename T>
struct floor_sum_2_info {
// pq : 01, 02, 11
std::array<T, 3> inner_floor_sum_2(T n, T m, T a, T b){
if (n <= 0) return {};
if (a == 0) return {};
T aquo = floor_div(a, m);
T arem = a - aquo * m;
T bquo = floor_div(b, m);
T brem = b - bquo * m;
if (aquo != 0 || bquo != 0){
auto rec = inner_floor_sum_2(n, m, arem, brem);
std::array<T, 3> ret = {};
// pq : 01
{
// ij : 00
ret[0] += bquo * n;
// ij : 01
ret[0] += aquo * (n * (n-1) / 2);
// ij : 10
ret[0] += rec[0];
}
// pq : 02
{
// ij : 00
ret[1] += bquo * bquo * n;
// ij : 01
ret[1] += aquo * bquo * n * (n-1);
// ij : 10
ret[1] += 2 * bquo * rec[0];
// ij : 02
ret[1] += aquo * aquo * ((n-1) * n / 2 * (2*n-1) / 3);
// ij : 11
ret[1] += 2 * aquo * rec[2];
// ij : 20
ret[1] += rec[1];
}
// pq : 11
{
// ij : 00
ret[2] += bquo * (n * (n-1) / 2);
// ij : 01
ret[2] += aquo * ((n-1) * n / 2 * (2*n-1) / 3);
// ij : 10
ret[2] += rec[2];
}
return ret;
}
T k = (a * (n-1) + b) / m;
auto rec = inner_floor_sum_2(k, a, m, m - b + a - 1);
std::array<T, 3> ret = {};
// pq : 01
{
ret[0] += n * k - rec[0];
}
// pq : 02
{
ret[1] += n * k * k - rec[0] - 2 * rec[2];
}
// pq : 11
{
// ret[2] += (n-1) * n / 2 * k + (rec[0] - rec[1]) / 2;
ret[2] += ((n-1) * n * k + rec[0] - rec[1]) / 2;
}
return ret;
}
};
} // namespace noya2::internal::floor_sum
// p >= 0, q >= 0
// sum[i in [0, n)] i^p floor(a * i + b / m)^q
template<Modint mint, int p, int q>
mint floor_sum_pq(long long n, long long m, long long a, long long b){
static noya2::internal::floor_sum::floor_sum_pq_info<mint,p+q> info;
return info.inner_floor_sum_pq(n, m, a, b)[noya2::internal::floor_sum::floor_sum_pq_info<mint,p+q>::template idx<p,q>];
}
// T = int, long long
// p >= 0, q >= 0, p + q
// sum[i in [0, n)] i^p floor(a * i + b / m)^q
template<typename T>
std::array<T, 3> floor_sum_2(T n, T m, T a, T b){
static noya2::internal::floor_sum::floor_sum_2_info<T> info;
return info.inner_floor_sum_2(n, m, a, b);
}
template<int i, int j>
struct say {
void operator()(auto ...args){
std::cout << i << ' ' << j << ' ' << powint<i+j>(args...) << std::endl;
}
};
template<int p, int q, int i, int j>
struct say4 {
void operator()(auto ...args){
std::cout << p << ' ' << q << ' ';
std::cout << i << ' ' << j << std::endl;
}
};
ull solve1(ull n, ull m, ull a, ull b1, ull b2){
if (a == 0){
return n*b1*b2;
}
if (b1 > b2) swap(b1,b2);
ull ans = 0;
ans += (n-1)*n/2*(2*n-1)/3 * a*a;
ans += (n-1)*n/2 * a*(b1+b2);
ans += b1*b2*n;
auto sb2 = floor_sum_2(n,m,a,b2);
ans -= sb2[0] * m * b1;
ans -= sb2[2] * m * a;
auto sb1 = floor_sum_2(n,m,a,b1);
ans -= sb1[0] * m * b2;
ans -= sb1[2] * m * a;
ull tot = 0;
[&]{
// return ;
ull k = floor_div(a*(n-1)+b1,m);
tot += sb1[1];
auto nsb1 = floor_sum_2(k,a,m,m-b1+a-1);
tot += nsb1[2];
auto nsb2 = floor_sum_2(k,a,m,m-b2+a-1);
tot -= nsb2[2];
tot += k * (n - min(n, ceil_div((k+1)*m-b2,a)));
}();
ans += tot * m * m;
return ans;
}
ll nn, mm, aa, bb;
template<int p, int q>
void f(){
using mint = modint998244353;
out(floor_sum_pq<mint,p,q>(nn+1,mm,aa,bb));
}
template<int p, typename qs>
struct callerpq;
template<int p, int ...qs>
struct callerpq<p, std::integer_sequence<int, qs...>> {
static void call(int q) {
((q == qs ? (f<p, qs>(), 0) : 0), ...);
}
};
template<typename ps, typename qs>
struct dispatcher;
template<int ...ps, int ...qs>
struct dispatcher<std::integer_sequence<int, ps...>, std::integer_sequence<int, qs...>> {
static void dispatch(int p, int q) {
((p == ps ? (callerpq<ps, std::integer_sequence<int, qs...>>::call(q), 0) : 0), ...);
}
};
void jikken3(){
int n; in(n);
using mint = modint998244353;
rep(i,n){
mint a = internal::floor_sum::power_sum<mint, 2>(i);
mint b = internal::floor_sum::floor_sum_pq_info<mint,2>::template coef<2,0> * mint(i).pow(0)
+ internal::floor_sum::floor_sum_pq_info<mint,2>::template coef<2,1> * mint(i).pow(1)
+ internal::floor_sum::floor_sum_pq_info<mint,2>::template coef<2,2> * mint(i).pow(2)
+ internal::floor_sum::floor_sum_pq_info<mint,2>::template coef<2,3> * mint(i).pow(3);
out(a,b);
}
}
void solve2(){
int p, q; in(p,q);
ll n, m, a, b; in(n,m,a,b);
nn = n;
mm = m;
aa = a;
bb = b;
using range = std::make_integer_sequence<int, 3>;
dispatcher<range, range>::dispatch(p, q);
}
void solve3(){
int p, q; in(p,q);
ll n, m, a, b; in(n,m,a,b);
using mint = modint998244353;
if (p + q <= 4){
auto ans = internal::floor_sum::floor_sum_pq_info<mint, 4>::inner_floor_sum_pq(n+1, m, a, b);
out(ans[internal::floor_sum::floor_sum_pq_info<mint, 4>::idx_func(p,q)]);
}
else {
exit(1);
// auto ans = internal::floor_sum::floor_sum_pq_info<mint, 20>::inner_floor_sum_pq(n+1, m, a, b);
// out(ans[internal::floor_sum::floor_sum_pq_info<mint, 20>::idx_func(p,q)]);
}
}
void solve(){
// jikken3(); return ;
// solve2(); return ;
solve3(); return ;
// ll n, m, a, b1, b2; in(n,m,a,b1,b2);
// out(ll(solve1(n,m,a,b1,b2)));
using mint = modint998244353;
out(internal::floor_sum::factmint<mint,2>);
out(internal::floor_sum::ifactmint<mint,2>);
out(internal::floor_sum::bernoulli<mint,2>);
int n; in(n);
rep(i,n){
out(i, internal::floor_sum::power_sum<mint, 0>(i), internal::floor_sum::power_sum<mint, 1>(i), internal::floor_sum::power_sum<mint, 2>(i), internal::floor_sum::power_sum<mint, 3>(i));
}
}
int main(){
int t = 1; in(t);
while (t--) { solve(); }
}