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 <iostream>
#include <vector>
using namespace std;
typedef long long ll;

const int MOD = 1000000007;

ll modpow(ll a,ll n){
  a%=MOD;
  ll res=1;
  while(n){
    if(n&1) res=res*a%MOD;
    a=a*a%MOD;
    n>>=1;
  }
  return res;
}

int main(){
  ll n,k;
  cin>>n>>k;
  ll cnt[100005];
  for(ll gcd=1;gcd<=k;gcd++){
    ll d=k/gcd;
    cnt[gcd]=modpow(d,n);
  }
  for(ll gcd=k;gcd>=1;gcd--){
    for(int i=2*gcd;i<=k;i+=gcd){
      cnt[gcd]=(cnt[gcd]-cnt[i]+MOD)%MOD;
    }
  }
  ll ans=0;
  for(ll gcd=1;gcd<=k;gcd++){
    ans=(ans+(gcd*cnt[gcd])%MOD)%MOD;
  }
  cout<<ans<<endl;
  return 0;
}






