#include<iostream>
#include<algorithm>
#include<vector>
#include<queue>
using namespace std;
typedef long long ll;
const ll mod=1e9+7;
ll pow(ll x,ll y){
  if(y==0) return 1;
  ll res=pow(x,y/2);
  res*=res;
  res%=mod;
  if(y%2==1) res*=x;
  return res%mod;
}
ll ans[100005]={0};
int main(){
  ll n,k;
  cin>>n>>k;
  ll res=0;
  for(ll m=k;m>=1;m--){
    ll a1=pow(k/m,n);
    for(ll i=2*m;i<=k;i+=m){
      a1-=ans[i];
      a1+=mod;
      a1%=mod;
    }
    ans[m]=a1;
    res+=a1*m;
    res%=mod;
  }
  cout<<res<<endl;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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<iostream>
#include<algorithm>
#include<vector>
#include<queue>
using namespace std;
typedef long long ll;
const ll mod=1e9+7;
ll pow(ll x,ll y){
  if(y==0) return 1;
  ll res=pow(x,y/2);
  res*=res;
  res%=mod;
  if(y%2==1) res*=x;
  return res%mod;
}
ll ans[100005]={0};
int main(){
  ll n,k;
  cin>>n>>k;
  ll res=0;
  for(ll m=k;m>=1;m--){
    ll a1=pow(k/m,n);
    for(ll i=2*m;i<=k;i+=m){
      a1-=ans[i];
      a1+=mod;
      a1%=mod;
    }
    ans[m]=a1;
    res+=a1*m;
    res%=mod;
  }
  cout<<res<<endl;
}

```