Submission #835145

#	Time	Username	Problem	Language	Result	Execution time	Memory
835145		RaulAndrei01	NoM (RMI21_nom)	C++14	100 / 100	96 ms	109312 KiB

Main

#include <iostream>


using namespace std;
using ll = long long;
const int NMAX = 2002;
const int MOD = 1e9 + 7;


ll dp[NMAX][NMAX];
ll c[2 * NMAX][2 * NMAX];
ll fact[2 * NMAX], ifact[2 * NMAX];


ll imod(ll x)
{
    ll rez = 1;
    for (int bit = 0; (1 << bit) <= MOD - 2; bit++)
    {
        if ((1 << bit) & (MOD - 2))
        {
            rez = (rez * x) % MOD;
        }
        x = (x * x) % MOD;
    }
    return rez;
}

ll aranj(int n, int k)
{
    return (fact[n] * ifact[n - k]) % MOD;
}

int main()
{
    int n, m; cin >> n >> m;
    for (int i = 1; i <= 2 * n; i++)
    {
        c[i][i] = c[i][0] = 1;
        for (int j = 1; j < i; j++)
        {
            c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % MOD;
        }
    }


    fact[0] = 1;
    for (int i = 1; i <= 2 * n; i++)
    {
        fact[i] = (fact[i - 1] * i) % MOD;
    }


    ifact[2 * n] = imod(fact[2 * n]);
    for (int i = 2 * n - 1; i >= 0; i--)
    {
        ifact[i] = (ifact[i + 1] * (1ll * i + 1)) % MOD;
    }

    dp[0][0] = 1;
    for (int i = 1; i <= n; i++)
    {
        dp[0][i] = 0;
    }

    for (int i = 1; i <= m; i++)
    {
        int ni = 2 * n / m + ((2 * n) % m >= i);

        for (int j = 0; j <= n; j++)
        {
            // calc dp[i][j]
            for (int k = 0; k <= min(ni / 2, j); k++)
            {
                dp[i][j] += ((dp[i - 1][j - k] * c[ni][k]) % MOD) * aranj(ni-k , k) % MOD;
                if (dp[i][j] >= MOD) dp[i][j] -= MOD;
            }
//            cout << i << ' ' << j << ' ' << dp[i][j] << '\n';
        }
    }

    ll bad = 0;
    ll p2 = 1;
    for (int i = 1; i <= n; i++)
    {
        p2 <<= 1;
        if (p2 >= MOD) p2 -= MOD;
        if (i % 2 == 0)
        {
            bad -= ((c[n][i] * fact[2 * n - 2 * i] % MOD) * dp[m][i]) % MOD * (fact[i] % MOD) % MOD;
            if (bad < 0) bad += MOD;
        }
        else {
            bad += ((c[n][i] * fact[2 * n - 2 * i] % MOD) * dp[m][i]) % MOD * (fact[i] % MOD) % MOD;
            if (bad >= MOD) bad -= MOD;
        }
    }

    ll ans = fact[2 * n];
    
    ans -= bad;
    if (ans < 0) ans += MOD;

    cout << ans << '\n';
}

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