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;

long long modpow(long long a, long long n, long long mod){
	long long ans = 1;

	while(n > 0){
		if(n & 1){
			ans = ans * a % mod;
		}
		a = a * a % mod;
		n >>= 1;
	}

	return ans;
}

const int modnum = 1000000007;

int main(){
	int n, k, x;
	long long ans = 0;

	cin >> n >> k;

	vector<long long> memo(k+5, 0);
	for(x=k; x>0; x--){
		long long div =  k / x;
		memo[x] = modpow(div, n, modnum);
		for(int i=2; i*x <= k; i++){
			memo[x] -= memo[i*x];
		}
		ans = (ans + x * memo[x] % modnum) % modnum;
	}

	while(ans < 0){
		ans += modnum;
	}

	cout << ans << endl;
}

