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.*;
import java.io.PrintWriter;
public class Main{
  public static long mod=1000000007;
  public static long Hoku(long a, long b){
    if(b==0){return 1;}
    else if(b%2==0){
      long k =Hoku(a,b/2);
      return k*k%mod;}
    else{long t=Hoku(a,b-1);
         return t*a%mod;}
  }
  public static void main(String[] args){
    Scanner sc =new Scanner(System.in);
    long N=sc.nextLong();
    int K =sc.nextInt();
    sc.close();
    long P[]=new long[K+1];
    long x=0;
    for(int i=K;i>0;i--){
      long j=K/i;
       P[i]=Hoku(j,N);
      for(int l=2;l<=j;l++){
        P[i]=P[i]-P[i*l];}
      x=(x+i*P[i])%mod;}
    System.out.println(x);
  }
}