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 int long long
#define p (int)(1e9 + 7)

int MOD(int a){
	return (a %= p) >= 0 ? a : a + p;
}

int power(int a, int N){
	if(N == 0){
		return 1;
	}
	else if(N % 2 == 0){
		return power(MOD(a * a), N / 2);
	}
	else{
		return MOD(a * power(a, N - 1));
	}
}

signed main(){
	int N, K, i, j, ans = 0;
	scanf("%lld%lld", &N, &K);
	vector<int> count(K + 1, 0);
	for(i = K; i >= 1; i--){
		count[i] = power(K / i, N);
		for(j = i + i; j <= K; j += i){
			count[i] = MOD(count[i] - count[j]);
		}
		ans = MOD(ans + i * count[i]);
	}
	printf("%lld\n", ans);
	return 0;
}