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 int maxn=1e5+5;
vector<ll> V;
const ll mod=1e9+7;
ll GCD[maxn];
inline ll fpow(ll a,ll b){
    ll ans=1;
    for(;b;b>>=1,a=a*a%mod) if(b&1) ans=ans*a%mod;
    return ans;
}
int main() {
    ll n,k,ans=0;cin>>n>>k;
    for(int i=k;i>=1;i--){
        GCD[i]=fpow(k/i,n);
        for(int j=2*i;j<=k;j+=i) GCD[i]=(GCD[i]-GCD[j]+mod)%mod;
        (ans+=GCD[i]*i)%=mod;
    }
    cout<<ans<<endl;
    return 0;
}