乘法逆元

Chosen by god

 。。。

 

 

 

#include <iostream>
#include <algorithm>
#include <cstdio>
#define re(i,m,n) for(int i=m;i<=n;i++)
typedef long long LL;
using namespace std;

const LL mod= 1e9+7;
const int N = 1e3+1;
LL fact[N], ifact[N], inv[N];
LL a[N];
void init(){
    fact[0]=1; re(i, 1,N) fact[i]=fact[i-1]*i%mod;
    inv[1]=1;  re(i, 2,N) inv[i]=(mod-mod/i)*inv[mod%i]%mod;
    ifact[0]=1;re(i, 1,N) ifact[i]=ifact[i-1]*inv[i]%mod;
}
LL Cnm(LL n, LL m){
    return fact[n]*ifact[n-m]%mod*ifact[m]%mod;
}
LL ans[N][N];
LL c[N][N];
LL e[N];
int main(){
    init();
    re(i,0,1000){
        c[i][0]=1;
        re(j,1,i)
            c[i][j]=(c[i][j-1]+Cnm(i,j))%mod;
    }
    e[0]=1;
    re(i, 1,1000) e[i]=e[i-1]*inv[2]%mod;
    re(i,1,1000){
        ans[i][0]=1;
        re(j,1,i)
            ans[i][j]=(c[i][i]-c[i][j-1]+mod)%mod*e[i]%mod;
    }
    int T;cin>>T;
    while(T--){
        int n, m;
        scanf("%d%d", &n,&m);
        printf("%lld\n", ans[n][m]);
    }
    return 0;
}