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;
const ll N=2e5+5,mod=1e9+7;
ll power(ll n,ll p){
    ll ans=1;
    while(p){
        if(p&1)ans*=n,ans%=mod;
        p>>=1;
        n*=n;
        n%=mod;
    }
    return ans;
}
ll sum[N],ans;
int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    ll n,k;cin>>n>>k;
    for(ll i=k;i>=1;i--){
        ll cnt=k/i;
        sum[i] = power(cnt,n);
        for(ll j=2*i;j<=k;j+=i)sum[i]=sum[i]-sum[j]+mod,sum[i]%=mod;
        ans+=(sum[i]*i)%mod;
        ans%=mod;
    }
    cout<<ans;
}