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>
#include <algorithm>
#include <vector>
const int MOD = 1e9 + 7;
typedef long long ll;
using namespace std;

ll modpow(ll a, ll n) {
	ll res = 1;
	while (n > 0) {
		if (n & 1) res = res * a % MOD;
		a = a * a % MOD;
		n >>= 1;
	}
	return res;
}

int main() {
	int n, k;
	cin >> n >> k;
	vector<ll> num(k + 1, 0);
	//num[k] = 1;
	//all_gcd がkとなるものは1つ
	for (ll i = k; i >= 1; i--) {
		num[i] = modpow(k / i, n);
		for (int j = i * 2; j <= k; j += i)
			num[i] -= num[j];
	}
	ll ans = 0;
	for (int i = 1; i <= k; i++) {
		ans += i * num[i] % MOD;
		ans %= MOD;
	}
	cout << ans << endl;
	return 0;
}