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 {

  static final long MOD = 1_000_000_007;

  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int k = sc.nextInt();
    long answer = 0;
    long[] array = new long[k + 1];
    for (int i = k; i >= 1; i--) {
      array[i] = myPow((long) k / i, n);
      for(int i2 = i * 2; i2 <= k; i2 += i){
        array[i] = (array[i] - array[i2]) % MOD;
      }
    }
    for (int i = 1; i <= k; i++) {
      long add = (array[i] * (long) i ) % MOD;
      answer = (answer + add) % MOD;
    }
    System.out.println(answer);
  }

  static long myPow(long x, int n) {
    long answer = 1l;
    while (n > 0) {
      if ((n & 1) == 1) {
        answer = answer * x % MOD;
      }
      x = x * x % MOD;
      n >>= 1;
    }
    return answer;
  }
}