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<stdio.h>
#include<stdlib.h>
#define  ll long long
#define MOD 1000000007

ll rui(ll a,ll b){
  a*=a;
  b--;
  if(b==0)return a;
  else rui(a,b);
};  

int main(){
  ll n,k,c,ans=0;
  scanf("%lld %lld",&n,&k);
  ll w[k+1];
  for(ll a=k;a!=0;a--){
    c=k/a;
    w[a]=rui(c,n)%MOD;
    for(ll j=2;j*a<=k;j++){
      w[a]-=w[a*j];
    };
    ans+=w[a]%MOD;
  };
  ans%=MOD;
  printf("%lld",ans);
};