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 C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

// stay fuckin hard -- Abhinav -IIITA
#include<bits/stdc++.h>
#define int long long
#define ld long double
using namespace std;
int mod=1e9;
ld pi=3.1415926535;
int fun(int a,int b){
	int r=1;
	while(b!=0){
		if(b&1){
			r*=a;
			r%=mod;
		}
		b/=2;
		a*=a; a%=mod;
	}
	return r;
}
int32_t main(){
	int n,k; cin>>n>>k;
	int ans=0;
	int dp[k+1]={0};
	for(int i=k;i>0;--i){
		dp[i]=fun((k/i),n);
		for(int ii=2*i;ii<=k;ii+=i)
			dp[i]-=dp[ii];
		ans+=i*dp[i]; ans%=mod;
	}
	cout<<ans;
	return 0;
}