【组合数】51Nod 1627 瞬间移动

题面在这里

考虑枚举移动的步数i

那么答案就是

∑i=1i<min(n,m)Ci−1n−2⋅Ci−1m−2

示例程序：

#include<cstdio>typedef long long ll;const int maxn=100005,tt=1e9+7;int n,m;ll fac[maxn],inv[maxn],ans;ll power(ll a,int b){    ll w=a,res=1;    while (b){        if (b&1) res=res*w%tt;        w=w*w%tt;        b>>=1;    }    return res;}void make(){    fac[0]=1;inv[0]=1;    for (int i=1;i<=100000;i++) fac[i]=fac[i-1]*i%tt,inv[i]=power(fac[i],tt-2);}inline ll C(int y,int x){    return fac[x]*inv[y]%tt*inv[x-y]%tt;}int main(){    scanf("%d%d",&n,&m);    if (n==2||m==2) return printf("1"),0;    make();ans=0;    for (int i=1;i<n&&i<m;i++)     (ans+=C(i-1,n-2)*C(i-1,m-2)%tt)%=tt;    printf("%lld",ans);    return 0;}