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.*;

public class Main {
    public static void main(String args[]){
        Scanner scanner = new Scanner(System.in);
        final int N = scanner.nextInt();
        final int K = scanner.nextInt();
        final int div = 1000000000 + 7;
        int[] count = new int[K+1];
        int[] memo = new int[K+1];
        for(int i=K; i>=1; i--){
            int n = K/i;
            if(memo[n]>0){
                count[i] = memo[n];
            }else{
                long c = 1;
                for(int j=0; j<N; j++){
                    c = c*n;
                    c = c%div;
                }
                count[i] = (int)c;
                memo[n] = (int)c;
            }
            for(int k=2; k<=n; k++){
                count[i] = count[i] + div - count[i*k];
                count[i] = count[i] % div;
            }
        }
        long res = 0;
        for(int i=1; i<=K; i++){
            long add = ((long)count[i]*(long)i) % div;
            res = (res + add) % div;
        }
        System.out.println(res);
    }
}