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>
#define rep(i,n) for(long long i = 0; i < (long long)(n); ++i)

using namespace std;
using ll = long long;

const ll mod = 7 + 1e9;

ll mpow (ll x, ll y) {
	ll a = 1;
	for (int i = 30; i >= 0; i--) {
		a = (a * a) % mod;
		if (y >> i & 1) {
			a = (a * x) % mod;
		}
	}
	return a;
}

int main() {
	ll n, k, ans = 0;
	cin >> n >> k;
	vector<ll> g(k + 1, 0);
	for (ll i = k; i > 0; i--) {
		g[i] = mpow(k / i, n);
		for (int v = 2; v * i <= k; v++) {
			g[i] -= g[v * i];
			if (g[i] < 0) g[i] += mod;
		}
		ans += g[i] * i;
		ans %= mod;
	}
	cout << ans << endl;
	return 0;
}
