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;
#define N 666666
#define int long long
#define mod 1000000007
int f(int a,int b){
	int s=1;
	while(b){
		if(b%2) s=(s*a)%mod;
		a=(a*a)%mod;
		b/=2;
	}
	return s;
}
int res[N];
signed main(){
	int n,k;
	cin>>n>>k;
	int ans=0;
	for(int i=k;i>=1;i--){
		res[i]=f(k/i,n);
		for(int j=2;j*i<=k;j++) res[i]-=res[i*j];
	}
	for(int i=1;i<=k;i++) ans=(ans+i*res[i])%mod;
	cout<<ans;
	return 0;
} 