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: Accepted)

import java.util.*;
import java.io.PrintWriter;
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();
		long ans=0;
		long[] kk=new long[k+1];
		for(int i=k; i>=1; i--){
			kk[i]=modpow(k/i,n);
			for(int j=2; j<=k/i; j++){
				kk[i]=(kk[i]-kk[i*j]+mod)%mod;;
			}
			ans=(ans+kk[i]*i)%mod;
		}
		System.out.println(ans);
	}
	static long modpow(long left,long right){
		long ans=1;
		while(right>0){
			if((right&1)==1){
				ans*=left;
			}
			right>>=1;
			left*=left;
			ans%=mod;
			left%=mod;
		}
		return ans;
	}
}