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 double db;
ll mod=1e9+7,num[100005];
ll qpow(ll a,ll b){
    ll res=1;
    while(b){
        if(b&1) res=res*a%mod;
        a=a*a%mod;
        b/=2; 
    }
    return res%mod;
}
int main(){
    ll n,k,ans=0;
    cin>>n>>k;
    for(ll i=k;i>=1;i--){
        num[i]=qpow(k/i,n);
        for(ll j=i*2;j<=k;j+=i){
            num[i]=(num[i]-num[j]+mod)%mod;
        }
        ans=(ans%mod+num[i]%mod*i%mod)%mod;
    }
    cout<<ans%mod<<endl;
}