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;
typedef long long INT;
INT C[100100];
INT Pow_Mod(INT I, INT J, INT mod){
	INT r = 1, i,j;
	for(i=1, j = I; i <= J ;i<<=1, j=(j*j)%mod)	if(i&J) r = (r*j)%mod;
	return r;
}
int main(){
	INT i, j, n, k, mod=1000000007, s=0;
	cin >> n >> k;
	for(i=k;i>0;i--){
		C[i] = Pow_Mod(k/i,n,mod);
		for(j=i+i;j<=k;j=j+i){
			C[i]=(C[i]-C[j]+mod)%mod;
		}
		s = (s+i*C[i])%mod;
	}	
	cout << s;
}