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;

long long mpow(long long x, int n) {
	long long r=1;
	while (n>0) {
		if (n&1) r=r*x%1000000007;
		x = x*x%1000000007;
		n >>= 1;
	}
	return r;
}

int main() {
	int n, k;
	cin >> n >> k;
	
	long long sumg = 0;
	long long cntg[100010];
	for (int i=k; 0<i; i--) {
		long long cntb = k/i;
		cntg[i] = mpow(cntb, n);
		for (int j=2; j*i<=k; j++) {
			cntg[i] += (1000000007-cntg[j*i]);
			cntg[i] %= 1000000007;
			if (cntg[i]<0) cout << 1;
		}
		sumg += cntg[i]*i;
		sumg %= 1000000007;
	}

	cout << sumg << endl;	

}
