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;
using ll = long long int;
#define rep(i, n) for(int i=0; i<(int)(n); ++i)

const int M = 1e9 + 7;
ll mod_pow(ll a, ll b) {
	ll ans = 1;
	while (b){
		if (b&1) ans = ans * a % M;
		a = a * a % M;
		b >>= 1;
	}
	return ans;
}
int main() {
	ios::sync_with_stdio(false);
	cin.tie(0), cout.tie(0);
	ll n, k;
	cin >> n >> k;
	vector<ll> c(k+1);
	for (ll i = k; i >= 1; --i) {
		c[i] = mod_pow(k / i, n);
		int j = 2;
		while (i * j <= k) {
			c[i] = (c[i] + M - c[i*j])%M;
			++j;
		}
	}
	ll ans = 0;
	rep(i, k+1) {
		ans += (c[i] * i % M);
		ans %= M;
	}
	cout << ans << endl;
}