How Many Sets I

Description

Give a set S, |S| = n, then how many ordered set group (S₁, S₂, ..., S_k) satisfies S₁ ∩ S₂ ∩ ... ∩ S_k = ∅. (S_i is a subset of S, (1 <= i <= k))

Input

The input contains multiple cases, each case have 2 integers in one line represent n and k(1 <= k <= n <= 2³¹-1), proceed to the end of the file.

Output

Output the total number mod 1000000007.

Sample Input

1 12 2

Sample Output

19

注意本题有序，就当做是序偶就行了！！从而推导公式ans=(2^k-1)^n

代码：

#include <algorithm>#include <iostream>#include <cstring>#include <cstdlib>#include <vector>#include <queue>#include <cstdio>#include <cmath>#include <string>#include <stack>#include <cctype>using namespace std;#define mod 1000000007long long fun(long long a,long long p,long long m){    if(p==0)        return 1;    long long r=a%m;    long long k=1;    while(p>1)    {        if((p&1)!=0)        {            k=(k*r)%m;        }        r=(r*r)%m;        p>>=1;    }    return (r*k)%m;}int main(){    long long n,k;    while(cin>>n>>k)    {        long long sum;        sum=fun(2,k,mod)-1;        long long temp;        temp=fun(sum,n,mod);        cout<<temp<<endl;    }    return 0;}