ZOJ 3556 How Many Sets I

How Many Sets I

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Time Limit: 2 Seconds      Memory Limit: 65536 KB

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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 1
2 2

Sample Output

1
9

题意：

个数为n的集合，从中选出K个子集使得他们的交集为空的个数。

　 子集可以重复选

考虑1个元素
它在k子集里的数目为2^k
其中有一种是k个子集都有这个元素，他们这k个子集的交集就不为空
所以1个元素k个子集交集为空的数目 有(2^k)-1 种
那么n个元素就是((2^k)-1）^n

#include<cstdio>
using namespace std;
typedef long long LL;
const LL mod=1000000007;
LL n,k;
LL pow(LL a,LL b)
{
    LL r=1;
    while(b)
    {
        if(b&1) r*=a,r%=mod;
        b>>=1; a*=a; a%=mod;
    }
    return r;
}
int main()
{
    while(scanf("%lld%lld",&n,&k)!=EOF) 
    printf("%lld\n",pow(pow(2,k)-1,n));
}