Description
Staginner , a wise coder , became a legendary soul after centuries later somehow . So one day he was summoned by a sorcerer , Gestapolur . The sorcerer said : I'm facing a hard problem and it's so obscure that even make me wanna going to die . So I summoned you for help.
The problem was described as following:
There are N(1<=N<=231-1) magic grails , each grail could have none or several magic properties . And there are K(1<=K<=N) magic properties .We supposed that all grails have property i are belong to set S_i . And because some mysterious reason , S1 ∩ S2 ∩ ... ∩ Sk must be empty. So how many grail-arrange scheme could satisfy these condition ?
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
思路：根據題意符合條件的情況有：
但是N非常非常的大，所以先求C=
代碼：
#include<iostream>
using namespace std;
#define MO 1000000007
int fab(int a,int b) //a^b%1000000007
{
if (b==1) return a;
long long c = fab(a, b / 2);//fab(a, b / 2)*fab(a, b / 2) % MO
c = c*c%MO;
c = (b % 2 == 1) ? c*a%MO : c;
return c;
}
int main()
{
int n, k;
while (cin >> n >> k)
{
int kk = fab(2, k) - 1;
cout << fab(kk, n) << endl;
}
return 0;
}