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;
#define all(V) V.begin(),V.end()
#define ll long long
#define MOD 1000000007

ll modpow(ll x, ll y) {
	ll ans = 1;
	while (y) {
		if (y & 1)ans *= x;
		x *= x;
		ans %= MOD;
		x %= MOD;
		y /= 2;
	}
	return ans;
}

ll res[100010];

int main() {
	int N, K;
	cin >> N >> K;
	ll ans = 0, cnt;
	for (int i = 0;i < 100010;i++)res[i] = 0;
	for (ll i = K;i >= 1;i--) {
		cnt = modpow(K / i, N);
		for (int j = i;j <= K;j += i) {
			cnt -= res[j];
			if (cnt < 0)cnt += MOD;
		}
		res[i] = cnt;
		ans += cnt * i;
		ans %= MOD;
	}
	cout << ans << endl;
}