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 int ll;
typedef pair<ll,ll> P;

#define MOD 1000000007  //E9

//a^n%m
ll modpow(ll a,ll n,ll m=MOD){
    ll r=1;
    while(n>0){
        if(n&1)r=r*a%m;
        a=a*a%m;
        n>>=1;
    }
    return r;
}
ll num[100001];

int main(){
    int n,k;
    cin>>n>>k;
    ll ans=0;
    for(int i=k;i>=1;i--){
        ll tnum=modpow(k/i,n);
        for(int a=i+i;a<=k;a=a+i){
            tnum=(tnum-num[a]+MOD)%MOD;
        }
        num[i]=tnum%MOD;
        ans=(ans+(tnum*i)%MOD)%MOD;
    }
    cout<<ans<<endl;

    return 0;
}