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>
typedef long long ll;
using namespace std;
const ll mod=1e9+7,maxn=1e6+7;
ll ksm(ll a,ll b){return b?ksm(a*a%mod,b/2)*(b%2?a:1)%mod:1;}
ll n,k;
ll dp[maxn];
int main(){
    cin>>n>>k;
    ll ans=0;
    for(int i=k;i>=1;i--){
        dp[i]=ksm(k/i,n);
        for(int j=2*i;j<=k;j+=i) dp[i]-=dp[j];
        ans=(ans+i*dp[i]%mod)%mod;
    }
    cout<<(ans+mod)%mod;
    return 0;
}
