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 <cstdio>
using namespace std;
const long long mod = 1e9 + 7;
long long n, k;
long long dp[100010], ans;
long long ksm(long long a, long long b) {
	long long ret = 1;
	while (b) {
		if (b & 1) {
			ret = (ret * a) % mod;
		}
		a = (a * a) % mod;
		b >>= 1;
	}
	return ret;
}
int main() {
	cin >> n >> k;
	for (long long i = k; i >= 1; i--) {
		long long num = k / i;
		dp[i] = ksm(num, n);
		for (long long j = i + i; j <= k; j += i) {
			dp[i] = (dp[i] - dp[j] + mod) % mod;
		}
		ans = (ans + dp[i] * i) % mod;
	}
	cout << ans;
	return 0;
}