#include <bits/stdc++.h>
#define ll long long
using namespace std;

ll mpower(ll a,ll b,ll c){
  int z;
  if(b==0){
    z=1;
    z%=c;
    return z;
  }
  if(b==1){
    z=a;
    z%=c;
    return z;
  }
  else{
    return (((mpower(a,b/2,c))*(mpower(a,b/2,c))%c)*mpower(a,b%2,c)%c);
  }
}

int main() {
  int n,k;
  cin>>n>>k;
  ll mod=1e9+7;
  ll vec[k+1];
  for(int i=k;i>0;i--){
    vec[i]=mpower(k/i,n,mod);
    for(int j=2;j<k+10;j++){
      if(i*j>k){
        break;
      }
      vec[i]-=vec[i*j];
    }
  }
  ll ans=0;
  for(int i=1;i<=k;i++){
    ans+=i*vec[i];
    ans%=mod;
  }
  cout<<ans<<endl;
}
### Prompt

Generate a cpp solution to the following problem:

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).

Examples

Input

3 2


Output

9


Input

3 200


Output

10813692


Input

100000 100000


Output

742202979

### Response

```cpp
#include <bits/stdc++.h>
#define ll long long
using namespace std;

ll mpower(ll a,ll b,ll c){
  int z;
  if(b==0){
    z=1;
    z%=c;
    return z;
  }
  if(b==1){
    z=a;
    z%=c;
    return z;
  }
  else{
    return (((mpower(a,b/2,c))*(mpower(a,b/2,c))%c)*mpower(a,b%2,c)%c);
  }
}

int main() {
  int n,k;
  cin>>n>>k;
  ll mod=1e9+7;
  ll vec[k+1];
  for(int i=k;i>0;i--){
    vec[i]=mpower(k/i,n,mod);
    for(int j=2;j<k+10;j++){
      if(i*j>k){
        break;
      }
      vec[i]-=vec[i*j];
    }
  }
  ll ans=0;
  for(int i=1;i<=k;i++){
    ans+=i*vec[i];
    ans%=mod;
  }
  cout<<ans<<endl;
}
```