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.util.*;
import static java.lang.Math.*;

public class Main {
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		
		// 入力
		int n = sc.nextInt();
		int k = sc.nextInt();
		
		// 計算
		long result = 0;
		int MOD = 1000000007;
		long[] list = new long[k+1];
		for(int i = 1; i < k+1; i++){
		    list[i] = pow(k/i, n, MOD);
		}
		for(int i = k; i >= 1; i--){
		    int cnt = 2;
		    while(i*cnt <= k){
		        list[i] = list[i] + MOD - list[i*cnt];
		        list[i] %= MOD;
		        cnt++;
		    }
		}
		for(int i = 1; i < k+1; i++){
		    result += list[i]*i%MOD;
		    result %= MOD;
		}
		
		// 出力
		System.out.println(result);
	}
	
	public static long pow(long a, long n, long MOD) {
		long res=1;
		while (n>0) {
			if ((n-n/2*2)==1) {
				res=(res*a)%MOD;
			}
			a=(a*a)%MOD;
			n>>=1;
		}
		return res%MOD;
	}
}
