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 <iostream>

using namespace std;

#define ll long long
#define RS 1000000007

ll pow_ll(ll, ll);

int main() {
	int n, k;
	ll x;
	ll i, j;
	ll ans = 0;
	ll st[100010];
	cin >> n >> k;
	for (i = k; i > 0; i--) {
		x = pow_ll (k / i, n);
		for (j = 2; j <= k; j++) {
			if (i*j > k)break;
			x -= st[i*j];
			while (x < 0)x += RS;
		}
		ans += x * i;
		st[i] = x;
		//cout << ans << endl;
		if (ans > RS)ans %= RS;
	}
	cout << ans;
	return 0;

}

ll pow_ll(ll a,ll b){
    if(b == 0)return 1;
	if (b % 2 == 0)return pow_ll(a * a % RS, b / 2) % RS;
	else return a * pow_ll(a, b - 1) % RS;
}