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
import java.math.BigInteger;
import java.util.*;
public class Main {

	static int MOD = 1000000007;
	
	static long modpow(int N, int K) {
		return BigInteger.valueOf(N).modPow(BigInteger.valueOf(K), BigInteger.valueOf(MOD)).longValue();
	}
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int K = sc.nextInt();
		long ans = 0;
		long[] x = new long[K+1];
		for(int i = K; i >= 1; i--) {
			x[i] = modpow(K/i, N);
			for(int j = i * 2; j <= K; j += i)
				x[i] -= x[j];
			ans = (ans + x[i] * i) % MOD;
		}
		while(ans < 0)
			ans += MOD;
		System.out.println(ans);
	}

}
