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 <iostream>

using namespace std;
typedef long long ll;
ll mod = 1000000007,num[100010];
ll pw(ll a, ll x){
    ll ret = 1;
    while(x){
        if(x&1) (ret *= a) %= mod;
        (a *= a) %= mod;
        x /= 2;
    }
    return ret;
}

int main(){
    ll i,j,n,k,ans = 0;
    cin >> n >> k;
    for(i=k;i>=1;i--){
        num[i] = pw(k/i,n);
        for(j=2*i;j<=k;j+=i){
            num[i] -= num[j];
            if(num[i]<0) num[i] += mod;
        }
    }
    for(i=1;i<=k;i++){
        (ans += i*num[i]%mod) %= mod;
    }
    cout << ans << endl;
}