Consider sequences \\{A_1,...,A_N\\} of length N consisting of integers between 1 and K (inclusive).

There are K^N such sequences. Find the sum of \gcd(A_1, ..., A_N) over all of them.

Since this sum can be enormous, print the value modulo (10^9+7).

Here \gcd(A_1, ..., A_N) denotes the greatest common divisor of A_1, ..., A_N.

Constraints

* 2 \leq N \leq 10^5
* 1 \leq K \leq 10^5
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N K


Output

Print the sum of \gcd(A_1, ..., A_N) over all K^N sequences, modulo (10^9+7).

Examples

Input

3 2


Output

9


Input

3 200


Output

10813692


Input

100000 100000


Output

742202979
#include <bits/stdc++.h>
using namespace std;
const int mod=1e9+7;
long long qpow(long long a,long long b) {
	long long ans=1;
	while(b>0) {
		if(b&1) ans=ans*a%mod;
		a=a*a%mod;
		b>>=1;
	}
	return ans;
}
int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	long long N,K,ans=0;
	cin>>N>>K;
	vector<long long>sum(K+1);
	for(int i=K;i>0;i--) {
		sum[i]=qpow(K/i,N);
		for(int j=2*i;j<=K;j+=i) sum[i]=(sum[i]-sum[j]+mod)%mod;
		ans=(ans+sum[i]*i%mod)%mod;
	}
	cout<<ans<<"\n";
	return 0;
}
