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 ll MOD = 1e9 + 7;

ll n, k, ans;

ll mypow(ll base, ll exp) {
	ll ret = 1;
	while (exp) {
		if (exp & 1) ret = ret * base % MOD;
		base = base * base % MOD;
		exp >>= 1;
	}
	return ret;
}

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