Problem:
Score : 500 points

Problem Statement

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).

Sample Input 1

3 2

Sample Output 1

9

\gcd(1,1,1)+\gcd(1,1,2)+\gcd(1,2,1)+\gcd(1,2,2)
+\gcd(2,1,1)+\gcd(2,1,2)+\gcd(2,2,1)+\gcd(2,2,2)
=1+1+1+1+1+1+1+2=9

Thus, the answer is 9.

Sample Input 2

3 200

Sample Output 2

10813692

Sample Input 3

100000 100000

Sample Output 3

742202979

Be sure to print the sum modulo (10^9+7).

Solution in Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {

    static long mod = 1000000007;
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();
        int k = sc.nextInt();
        memo = new int[k+1];

        long res = 0;
        long[] num = new long[k+1];
        for(int i=k; i>=1; i--) {
            long a = b(k / i, n);
            for(int b = 2; i * b <= k; b++) {
                a += mod - num[i * b];
            }
            num[i] = a;
            res += num[i] * i;
            res %= mod;
        }

        System.out.println(res);
    }

    static int[] memo;

    static int b(int a, int b) {
        if(memo[a] > 0) return memo[a];
        long res = 1;
        for(int i=0; i<b; i++) {
            res *= a;
            res %= mod;
        }
        return memo[a] = (int)res;
    }


}