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;
#define ll long long
const int mod=1e9+7;
const int N=1e5+5;
ll cnt[N];
ll n,k,ans;

ll pow(ll num){
    ll res=1,m=n;
while(m>0){
    if(m&1)
    res=res*num%mod;
    num=num*num%mod;
    m>>=1;
}
//cout<<res<<'.'<<endl;
return res;
}

int main(){
ios::sync_with_stdio(0);
cin>>n>>k;
for(ll i=k;i>=1;i--){
    cnt[i]=pow(k/i);
    for(ll j=2;j*i<=k;j++){
        cnt[i]-=cnt[j*i];
    }
    ans+=(mod+(cnt[i]*i)%mod)%mod;
    ans=(ans+mod)%mod;
    //cout<<ans<<endl;
}
cout<<ans<<endl;
return 0;
}