結果

問題 No.2996 Floor Sum
ユーザー 👑 Nachia
提出日時 2025-04-23 01:07:58
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 431 ms / 5,000 ms
コード長 5,858 bytes
コンパイル時間 1,157 ms
コンパイル使用メモリ 86,216 KB
実行使用メモリ 7,844 KB
最終ジャッジ日時 2025-04-23 01:08:01
合計ジャッジ時間 3,107 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2
other AC * 12
権限があれば一括ダウンロードができます

ソースコード

diff # 

#ifdef NACHIA
#define _GLIBCXX_DEBUG
#else
#define NDEBUG
#endif
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(i64 i=0; i<i64(n); i++)
const i64 INF = 1001001001001001001;
template<typename A> void chmin(A& l, const A& r){ if(r < l) l = r; }
template<typename A> void chmax(A& l, const A& r){ if(l < r) l = r; }
using namespace std;

#include <utility>

#include <cassert>
namespace nachia{

// ax + by = gcd(a,b)
// return ( x, - )
std::pair<long long, long long> ExtGcd(long long a, long long b){
    long long x = 1, y = 0;
    while(b){
        long long u = a / b;
        std::swap(a-=b*u, b);
        std::swap(x-=y*u, y);
    }
    return std::make_pair(x, a);
}

} // namespace nachia

namespace nachia{

template<unsigned int MOD>
struct StaticModint{
private:
    using u64 = unsigned long long;
    unsigned int x;
public:

    using my_type = StaticModint;
    template< class Elem >
    static Elem safe_mod(Elem x){
        if(x < 0){
            if(0 <= x+MOD) return x + MOD;
            return MOD - ((-(x+MOD)-1) % MOD + 1);
        }
        return x % MOD;
    }

    StaticModint() : x(0){}
    StaticModint(const my_type& a) : x(a.x){}
    StaticModint& operator=(const my_type&) = default;
    template< class Elem >
    StaticModint(Elem v) : x(safe_mod(v)){}
    unsigned int operator*() const { return x; }
    my_type& operator+=(const my_type& r) { auto t = x + r.x; if(t >= MOD) t -= MOD; x = t; return *this; }
    my_type operator+(const my_type& r) const { my_type res = *this; return res += r; }
    my_type& operator-=(const my_type& r) { auto t = x + MOD - r.x; if(t >= MOD) t -= MOD; x = t; return *this; }
    my_type operator-(const my_type& r) const { my_type res = *this; return res -= r; }
    my_type operator-() const noexcept { my_type res = *this; res.x = ((res.x == 0) ? 0 : (MOD - res.x)); return res; }
    my_type& operator*=(const my_type& r){ x = (u64)x * r.x % MOD; return *this; }
    my_type operator*(const my_type& r) const { my_type res = *this; return res *= r; }
    bool operator==(const my_type& r) const { return x == r.x; }
    my_type pow(unsigned long long i) const {
        my_type a = *this, res = 1;
        while(i){ if(i & 1){ res *= a; } a *= a; i >>= 1; }
        return res;
    }
    my_type inv() const { return my_type(ExtGcd(x, MOD).first); }
    unsigned int val() const { return x; }
    int hval() const { return int(x > MOD/2 ? x - MOD : x); }
    static constexpr unsigned int mod() { return MOD; }
    static my_type raw(unsigned int val) { auto res = my_type(); res.x = val; return res; }
    my_type& operator/=(const my_type& r){ return operator*=(r.inv()); }
    my_type operator/(const my_type& r) const { return operator*(r.inv()); }
};

} // namespace nachia
using Modint = nachia::StaticModint<998244353>;


struct Unit {
    i64 x;
    i64 y;
    i64 P;
    i64 Q;
    vector<Modint> A;
    Modint& at(i64 p, i64 q){ return A[p * Q + q]; }
    Modint at(i64 p, i64 q) const { return A[p * Q + q]; }
};

vector<Modint> ifact, fact;


Unit shiftX(const Unit& r, i64 x){
    i64 P = r.P, Q = r.Q;
    Unit res = { r.x, r.y, P, Q, vector<Modint>(P*Q) };
    vector<Modint> XP(P,1);
    rep(i,P-1) XP[i+1] = XP[i] * (x-i) / (i+1);
    rep(p,P) rep(q,Q) rep(pp,p+1) res.at(p,q) += r.at(pp,q) * XP[p-pp];
    return res;
}
Unit shiftY(const Unit& r, i64 x){
    i64 P = r.P, Q = r.Q;
    Unit res = { r.x, r.y, P, Q, vector<Modint>(P*Q) };
    vector<Modint> XP(Q,1);
    rep(i,Q-1) XP[i+1] = XP[i] * (x-i) / (i+1);
    rep(p,P) rep(q,Q) rep(qq,q+1) res.at(p,q) += r.at(p,qq) * XP[q-qq];
    return res;
}

Unit merge(const Unit& l, const Unit& r){
    i64 P = min(l.P, r.P), Q = min(l.Q, r.Q);
    Unit res = { l.x + r.x, l.y + r.y, P, Q };
    res.A.resize(P * Q);
    rep(p,P) rep(q,Q) res.at(p,q) = r.at(p,q);
    res = shiftX(res, l.x);
    res = shiftY(res, l.y);
    rep(p,P) rep(q,Q) res.at(p,q) += l.at(p,q);
    return res;
}

Unit pow(const Unit& a, i64 i){
    if(i == 0) return Unit{ 0, 0, a.P, a.Q, vector<Modint>(a.P*a.Q) };
    if(i == 1) return a;
    auto r = pow(merge(a,a), i/2);
    return (i%2 == 1) ? merge(a,r) : r;
}

void testcase(){
    i64 P, Q, N, M, A, B; cin >> P >> Q >> N >> M >> A >> B;
    i64 offset_B = B / M; B %= M;
    if(B < 0){ offset_B -= 1; B += M; }
    i64 neg = A < 0 ? -1 : 1;
    if(neg == -1){ B = M - 1 - B; A = -A; }
    N += 1;
    Unit X = Unit{ 1, 0, P+1, Q+1, vector<Modint>((P+1)*(Q+1)) };
    Unit Y = Unit{ 0, neg, P+1, Q+1, vector<Modint>((P+1)*(Q+1)) };
    X.at(0,0) = 1;
    Unit L = Unit{ 0, 0, P+1, Q+1, vector<Modint>((P+1)*(Q+1)) };
    Unit R = Unit{ 0, 0, P+1, Q+1, vector<Modint>((P+1)*(Q+1)) };
    i64 C = (A * N + B) / M;
    while(true){
        i64 qa = A / M; A %= M;
        i64 qb = B / M; B %= M;
        X = merge(X, pow(Y, qa));
        L = merge(L, pow(Y, qb));
        C -= qa * N + qb;
        if(C == 0){ L = merge(merge(L, pow(X, N)), R); break; }
        i64 D = (M * C - B - 1) / A + 1;
        R = merge(merge(Y, pow(X, N - D)), R);
        B = M - B - 1 + A; swap(M, A); N = C - 1; C = D; swap(X, Y);
    }
    L = shiftY(L, offset_B);
    vector<Modint> F(P+1); F[0] = 1;
    rep(i,P) for(i64 j=i; j>=0; j--){ F[j+1] += F[j]; F[j] *= j; }
    vector<Modint> G(Q+1); G[0] = 1;
    rep(i,Q) for(i64 j=i; j>=0; j--){ G[j+1] += G[j]; G[j] *= j; }
    Modint ans = 0;
    rep(i,P+1) rep(j,Q+1) ans += L.at(i, j) * fact[i] * fact[j] * F[i] * G[j];
    cout << ans.val() << "\n";
}

int main(){
    ios::sync_with_stdio(false); cin.tie(nullptr);
    i64 Z = 100;
    ifact.assign(Z+1, 1);
    for(i64 i=1; i<=Z; i++) ifact[i] = ifact[i-1] / i;
    fact.assign(Z+1, 1);
    for(i64 i=1; i<=Z; i++) fact[i] = fact[i-1] * i;
    i64 T; cin >> T; rep(t,T) testcase();
    return 0;
}
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