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;

const int MOD = 1000000007;

ll poww(ll a, ll b) {
	if (b == 0) {
		return 1;
	}
	if (b & 1) {
		return (a * poww(a, b - 1)) % MOD;
	}
	return poww((a * a) % MOD, b >> 1);
}

int main() {
	ios::sync_with_stdio(false);
	int n, k;
	cin >> n >> k;
	vector<ll> cnt(k + 1);
	ll ans = 0;
	for (int g = k; g > 0; --g) {
		cnt[g] = poww(k / g, n);
		for (ll j = 2; g * j <= k; ++j) {
			cnt[g] -= cnt[g * j];
			if (cnt[g] < 0) {
				cnt[g] += MOD;
			}
		}
		ans += g * cnt[g];
		ans %= MOD;
	}
	cout << ans << endl;
}