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 <vector>

using namespace std;

#define MOD 1000000007

long long llpow(long long x, long long n) {
	if (!n) return 1;
	if (n & 1) return llpow(x * x % MOD, n >> 1) * x % MOD;
	return llpow(x * x % MOD, n >> 1);
}

int main() {
	int n, k; cin >> n >> k;
	vector<long long> cnt(k + 1);
	for (int i = 1; i <= k; ++i) cnt[i] = llpow(k / i, n);
	for (int i = k / 2; i > 0; --i)
		for (int j = i * 2; j <= k; j += i)
			cnt[i] = (cnt[i] - cnt[j] + MOD) % MOD;
	long long ans = 0;
	for (int i = 1; i <= k; ++i) (ans += cnt[i] * i % MOD) %= MOD;
	cout << ans << endl;

	return 0;
}