swust oj 2516 教练我想学算术 dp+组合计数

#include<stdio.h>
#include<string.h>
#include<iostream>
#include<string>
#include<queue>
#include<cmath>
#include<map>
#include<algorithm>
#include<vector>
//#define debug
using namespace std;
const int inf = 0x3fffffff;
const int mod = 1000000007;
const int mmax  = 1000010;
typedef long long LL;
int n,m,k;
LL inv[mmax];
LL jie[mmax];
LL dp[1100];
void pre()
{
    inv[0]=inv[1]=1;
    jie[0]=jie[1]=1;
    for(int i=2;i<mmax;i++)
    {
        inv[i]=(LL)(mod-mod/i)*inv[mod%i]%mod;
        jie[i]=jie[i-1]*i;
        jie[i]%=mod;
    }
    for(int i=2;i<mmax;i++)
    {
        inv[i]*=inv[i-1];
        inv[i]%=mod;
    }

}
LL Pow_mod(LL x ,int n)
{
    LL res=1,tmp=x;
    for(;n;n/=2)
    {
        if(n&1)
            res=(res*tmp)%mod;
        tmp=(tmp*tmp)%mod;
    }
    return res;
}
LL C(int x,int y)
{
    if(y>x)
        return 0;
    return jie[x]*inv[y]%mod*inv[x-y]%mod;
}
void build()
{
    dp[0]=0;
    dp[1]=1;
    for(int i=2;i<=n;i++)
    {
        dp[i]=Pow_mod(i,n);
        for(int j=1;j<i;j++)
        {
            dp[i]-=dp[i-j]*C(i,j)%mod;
            dp[i]=(dp[i]%mod+mod)%mod;
        }
    }
}
int main()
{
    pre();
    while(~scanf("%d %d %d",&n,&m,&k))
    {
        if(m==1)
        {
            printf("%lld
",Pow_mod(k,n));
            continue;
        }
        build();
        LL cnt=0;
        for(int i=0;i<=n;i++)
        {
            for(int j=0;i+j<=n;j++)
            {
                LL tmp=1;
                tmp=C(k,i)*C(k-i,j)%mod*C(k-i-j,j)%mod;
                tmp*=dp[i+j]*dp[i+j]%mod*Pow_mod((LL)i,n*(m-2))%mod;
                tmp%=mod;
                cnt+=tmp;
                cnt%=mod;
            }
        }
        printf("%lld
",cnt);
    }
    return 0;
}