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)

#include <iostream>
#include <algorithm>

#define MOD 1000000007

using namespace std;

long q_pow(long x, long n){
    if(n == 0) return 1;
    if(n==1) return x;
    else if(n%2 == 0) return q_pow(x*x%MOD, n/2);
    else return x * q_pow(x, n-1) % MOD;
}

int main(){
   long N, K;
   cin >> N >> K; 
   long ans = 0;
   for(long div = 1; div <= K; div++){
       long up = K / div;
       long low = K / (div + 1) + 1;
       long add = (up + low) * (up - low + 1) / 2;
       add %= MOD;
       add *= (q_pow(div, N) - q_pow(div - 1, N) + MOD) ;
       add %= MOD;
       ans += add;
       ans %= MOD;
   }
   cout << ans << endl;
   return 0;
}