CodeForces - 1236B (a simple combination of mathematics)

The meaning of problems

There are n kinds of goods and m backpack, there are an infinite number of each article, now a number of these items into a backpack, to meet:

1, each of the backpack can not be the same kind of articles occurs (backpack allowing free);

2, all m backpack, each article have appeared.

Seeking the number of programs to 10 ^ 7 + 9 mod.

Thinking

Consider each item appears in each backpack, then for items i, there are 2 ^ m in the program, because at least then each item you want to appear in all backpack once, so the whole scheme does not appear to be subtracted, so that 2 ^ m - 1, there are n items, then it is (2 ^ m -1) ^ n

Code

 

#include<bits/stdc++.h>
using namespace std;
#define inf 0x3f3f3f3f
#define ll long long
const int N=200005;
const int mod=1e9+7;
const double eps=1e-8;
const double PI = acos(-1.0);
#define lowbit(x) (x&(-x))
ll gcd(ll a,ll b){return b==0?a:gcd(b,a%b);}
ll qpow(ll a,ll b){ll res=1;while(b){if(b&1) res=res*a%mod;a=a*a%mod;b>>=1;}return res;}
ll inv(ll a,ll p){return qpow(a,p-2);}
int main ()
{
    std::ios::sync_with_stdio(false);
    ll n,m;
    cin>>n>>m;
    cout<<qpow((qpow(2,m)-1+mod)%mod,n)<<endl;
    return 0;
}