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.Scanner;

public class Main {
    public static void main(String [] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int k = scanner.nextInt();
        long mod = 1000000007L;
        long sum = 0;
        long[] times = new long[k + 1];
        for (int gcd = k; gcd >= 1; --gcd) {
            long currentTimes = pow(k/gcd, n, mod);
            for (int i = 2 * gcd; i <= k; i += gcd) {
                currentTimes = (currentTimes - times[i] + mod) % mod;
            }
            times[gcd] = currentTimes;
            sum += gcd * currentTimes % mod;
            sum %= mod;
        }
        System.out.println(sum);

    }

    public static long pow(long base, long exp, long mod) {
        if (exp == 0) {
            return 1;
        }
        long half = pow(base, exp / 2, mod);
        if (exp % 2 == 0) {
            return half * half % mod;
        } else {
            return ((half * half % mod) * base % mod) % mod;
        }
    }
}
