Submission #858226

#	Time	Username	Problem	Language	Result	Execution time	Memory
858226		thangdz2k7	NoM (RMI21_nom)	C++17	100 / 100	112 ms	87124 KiB

Main

#include <bits/stdc++.h>
#define ii pair <int, int>
#define F first
#define S second

using namespace std;

const int mod = 1e9 + 7;
const int N = 4e3 + 5;

void add(int &a, int b){
    a += b;
    if (a >= mod) a -= mod;
    if (a < 0) a += mod;
}

int mu(int a, int b){
    if (b == 0) return 1;
    if (b % 2 == 1) return 1ll * mu(a, b - 1) * a % mod;
    int c = mu(a, b / 2);
    return 1ll * c * c % mod;
}

int dp[N][N], C[N][N];
int n, m;
int gt[N], re_2[N], re_gt[N];

int c(int b, int a){
    return 1ll * (1ll * gt[a] * re_gt[b] % mod) * re_gt[a - b] % mod;
}

void solve(){
    cin >> n >> m;
    gt[0] = 1;
    re_gt[0] = 1;
    for (int i = 1; i <= 2 * n; ++ i) {
        gt[i] = 1ll * gt[i - 1] * i % mod;
        re_gt[i] = mu(gt[i], mod - 2);
    }
    int kk = mu(2, mod - 2);
    re_2[0] = 1;
    for (int i = 1; i <= n; ++ i) re_2[i] = 1ll * re_2[i - 1] * kk % mod;

    for (int i = 0; i <= 2 * n; ++ i) for (int j = 0; j <= i; ++ j) C[j][i] = c(j, i);

    dp[0][0] = 1;
    for (int i = 1; i <= m; ++ i){
        int val = (2 * n - i) / m + 1;
        for (int j = 0; j <= n; ++ j){
            //dp[i][j] = dp[i - 1][j];
            for (int k = 0; k <= min(j, val / 2); ++ k){
                int zk = 1ll * dp[i - 1][j - k] * C[2 * k][val] % mod;
                //zk = 1ll * zk * re_2[k] % mod;
                zk = 1ll * zk * gt[2 * k] % mod;
                zk = 1ll * zk * C[k][n - j + k] % mod;
                add(dp[i][j], zk);
            }
            //cout << dp[i][j] << ' ';
        }
        //cout << endl;
    }

    int ans = 0;
    for (int i = 0; i <= n; ++ i){
        int val = 1ll * dp[m][i] * gt[(n - i) * 2] % mod;
        //val = 1ll * val * re_2[n - i] % mod;
        if (i % 2 == 0) add(ans, val);
        else add(ans, -val);
    }

    cout << ans;
}

int main(){
    //freopen("code.inp", "r", stdin);
    //freopen("code.out", "w", stdout);
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    int t = 1;
    while (t --) solve();

    return 0;
}

• Subtask 1: 9 / 9
• Subtask 2: 12 / 12
• Subtask 3: 13 / 13
• Subtask 4: 18 / 18
• Subtask 5: 48 / 48