Submission #857098

#	Time	Username	Problem	Language	Result	Execution time	Memory
857098		alexdd	NoM (RMI21_nom)	C++17	100 / 100	78 ms	31828 KiB

Main

#include<bits/stdc++.h>
using namespace std;
#define int long long
const int MOD = 1e9+7;
int n,m;
int dp[2005][2005];
int cntr[2005];
int pref[2005];
int fact[10005];
int invf[5005];
int put2[5005];
int put(int a, int exp)
{
    if(exp==0)
        return 1;
    if(exp%2==0)
        return put((a*a)%MOD,exp/2);
    else
        return (put((a*a)%MOD,exp/2)*a)%MOD;
}
int comb(int x, int y)
{
    if(x<y)
        return 0;
    return ((((fact[x]*invf[y])%MOD)*invf[x-y])%MOD);
}
signed main()
{
    cin>>n>>m;
    for(int i=1;i<=2*n;i++)
        cntr[i%m+1]++;
    fact[0]=1;
    put2[0]=1;
    for(int i=1;i<=5001;i++)
    {
        fact[i]=(fact[i-1]*i)%MOD;
        put2[i]=(put2[i-1]*2LL)%MOD;
    }
    invf[5001] = put(fact[5001], MOD-2);
    for(int i=5000;i>=0;i--)
        invf[i]=(invf[i+1]*(i+1))%MOD;
    dp[0][0]=1;
    for(int i=1;i<=m;i++)
    {
        pref[i]=(pref[i-1]+cntr[i])%MOD;
        for(int cntp=0;cntp<=pref[i]/2;cntp++)
        {
            dp[i][cntp]=0;
            for(int x=0;x<=min(cntp,cntr[i]);x++)
            {
                dp[i][cntp] += (((((dp[i-1][cntp-x] * fact[cntr[i]])%MOD) * comb(pref[i-1] - 2*(cntp-x), x))%MOD) * (put2[cntr[i]-x] * comb(n - (pref[i-1] - 2*(cntp-x) - x) - (cntp-x) - x, cntr[i]-x)%MOD))%MOD;
                dp[i][cntp] %= MOD;
            }
            //cout<<i<<" "<<cntp<<"  "<<dp[i][cntp]<<"\n";
        }
    }
    cout<<dp[m][n];
    return 0;
}
/**

dp[i][cntp] = numarul de moduri de a plasa pietre pe primele i resturi a.i. sa fi plasat cntp perechi de pietre
cntr[i] = nr de pozitii cu restul i
pref[i] = sum(cntr[x]), x = 1..i
dp[i][cntp] = sum(dp[i-1][cntp-x] * fact[cntr[i]] * comb(pref[i-1] - 2*cntp, x) * comb(n - (pref[i-1] - 2*cntp - x) - cntp - x, cntr[i]-x)


*/

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