luoguP1313 计算系数 题解(NOIP2011)

P1313 计算系数 题目

#include<iostream>
#include<cstdlib>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<algorithm>
#include<iomanip>
#include<ctime>
#include<queue>
#include<stack>
#define rg register
#define lst long long
#define N 1050
#define mod 10007
using namespace std;

lst a,b,k,n,m,ans;
lst f[N][N];

inline lst read()
{
    rg lst s=0,m=1;rg char ch=getchar();
    while(ch!='-'&&(ch<'0'||ch>'9'))ch=getchar();
    if(ch=='-')m=-1,ch=getchar();
    while(ch>='0'&&ch<='9')s=(s<<3)+(s<<1)+ch-'0',ch=getchar();
    return s*m;
}

inline lst qpow(rg lst x,rg lst y)
{
    rg lst res=1,base=x;
    while(y)
    {
        if(y&1)res=(res*base)%mod;
        base=(base*base)%mod;
        y>>=1;
    }
    return res;
}

int main()
{
    a=read(),b=read(),k=read(),n=read(),m=read();
    ans=(qpow(a,n)*qpow(b,m))%mod;

    f[1][1]=1;
    for(rg lst i=2;i<=k+1;++i)
        for(rg lst j=1;j<=i;++j)
        {
            f[i][j]=(f[i-1][j-1]+f[i-1][j])%mod;
        }
    if(n+m==k)
    {
        ans=(ans*f[k+1][k-n+1])%mod;
    }
    else ans=0;
    cout<<ans<<endl;
    return 0;
}