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
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
#define rep(i,m,n) for(int i=m;i<n;i++)
ll mod=1e9+7;

ll power(ll x,ll n){
    if(n==0) return 1;
    ll res=power(x*x%mod,n/2);
    if(n&1) res=res*x%mod;
    return res;
}

int main(){
  int n,k;
  cin>>n>>k;
  ll ans=0;
  ll cur[k+1];
  for(int i=k;i>0;i--){
    ll now=0;
    for(int j=2*i;j<=k;j+=i){
      now+=cur[j];
      now%=mod;
    }
    ll res=power(k/i,n)-now;
    if(res<0) res+=mod;
    cur[i]=res;
    ans+=i*res;
    ans%=mod;
  }
  cout<<ans<<endl;
}