結果

問題 No.2362 Inversion Number of Mod of Linear
ユーザー 👑 Nachia
提出日時 2023-06-24 01:18:32
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 295 ms / 2,000 ms
コード長 3,053 bytes
コンパイル時間 952 ms
コンパイル使用メモリ 86,568 KB
最終ジャッジ日時 2025-02-15 01:49:02
ジャッジサーバーID
（参考情報） 		judge2 / judge5
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 * 8
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 #
プレゼンテーションモードにする

#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <atcoder/modint>
#include <atcoder/math>
using namespace std;
using i32 = int;
using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(int i=0; i<(int)(n); i++)
const i64 INF = 1001001001001001001;
using Modint = atcoder::static_modint<998244353>;
template<class modint>
modint TriangleSumTimesLinear(
    long long n,
    long long a,
    long long b,
    modint c,
    modint d,
    modint e
){
    if(n <= 0) return modint(0);
    if(a < b) return TriangleSumTimesLinear(n, b, a, d, c, e);
    modint res = 0;
    static const modint inv2 = modint(2).inv();
    static const modint inv6 = modint(6).inv();
    while(true){
        if(n <= 0) break;
        if(a < b){ swap(a,b); swap(c,d); continue; }
        
        // eliminate triangle
        i64 maxi = (n - 1) / a + 1;
        i64 t = min<i64>(a / b, (n - 1) % a / b + 1);
        res += c * maxi * (maxi-1) * (maxi+1) * inv6 * t;
        res -= d * maxi * (maxi-1) * (maxi+1) * inv6 * t * (t-1) * inv2;
        res += d * maxi * maxi * (maxi+1) * inv2 * t * (t-1) * inv2;
        res += d * maxi * (maxi-1) * (maxi+1) * inv6 * t;
        res += e * maxi * (maxi+1) * inv2 * t;
        n -= maxi * b * t;
        a -= b * t;
        c -= d * t;
        e += d * maxi * t;
    }
    return res;
}
template<class modint>
modint AKindOfFloorSum(
    long long n,
    long long m,
    long long a,
    long long b
){
    long long q = b / m;
    modint tmp = modint(n) * modint(n-1) / 2 * q;
    b -= q * m;
    long long newn = a * (n-1) + b - (m-1);
    if(newn <= 0) return 0;
    return tmp + TriangleSumTimesLinear<modint>(newn, a, m, -1, 0, n-1);
}
template<class modint>
modint BKindOfFloorSum(
    long long n,
    long long m,
    long long a,
    long long b
){
    long long q = b / m;
    modint tmp = modint(n) * q;
    b -= q * m;
    long long newn = a * (n-1) + b - (m-1);
    if(newn <= 0) return 0;
    return tmp + TriangleSumTimesLinear<modint>(newn, a, m, 0, 0, 1);
}
using Modint1 = atcoder::static_modint<1000000007>;
using Modint2 = atcoder::static_modint<1000000009>;
template<class modint>
modint find_mod(
    long long N,
    long long M,
    long long X,
    long long Y
){
    modint x1 = AKindOfFloorSum<modint>(N, M, X, Y) * 2;
    modint x2 = BKindOfFloorSum<modint>(N, M, X, Y) * (1-N);
    modint x3 = AKindOfFloorSum<modint>(N, M, X, 0);
    modint x4 = BKindOfFloorSum<modint>(N, M, X, 0) * (-N);
    return x1 + x2 + x3 + x4;
}
int main(){
    int T; cin >> T;
    rep(t,T){
        long long N,M,X,Y; cin >> N >> M >> X >> Y;
        auto x1 = find_mod<Modint1>(N, M, X, Y);
        auto x2 = find_mod<Modint2>(N, M, X, Y);
        long long ans = atcoder::crt({ x1.val(), x2.val() }, { x1.mod(), x2.mod() }).first;
        cout << ans << '\n';
    }
    return 0;
}
struct ios_do_not_sync{
    ios_do_not_sync(){
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
    }
} ios_do_not_sync_instance;
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