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 ll;
const int mod = 1000000007;
ll modpow(ll n, int k) {
	ll r = 1;
	while (k > 0) {
		if (k&1) (r *= n) %= mod;
		(n *= n) %= mod;
		k >>= 1;
	}
	return r;
}
int main() {
	int N, K;
	cin >> N >> K;
	vector<ll> a(K+1);
	ll res = 0;
	for (int k = K; k >= 1; -- k) {
		ll r = modpow(K/k, N);
		for (int i = 2*k; i <= K; i += k) {
			r = (r+mod-a[i])%mod;
		}
		a[k] = r;
		res = (res + r * k) % mod;
	}
	cout << res << endl;
}
