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 = 100000;
const LL MOD = (LL)1e9+7;

int N, K;
LL dp[MAXN+5], ans;

LL power(LL a,LL b){
    return b ? power(a*a%MOD,b/2)*(b%2?a:1)%MOD : 1;
}

int main(){
    ios_base::sync_with_stdio(0); cin.tie(0);
    cin >> N >> K;
    for (LL i = K; i >= 1; --i){
        dp[i] = power(K/i, N);
        for (LL j = 2 * i; j <= K; j += i) {
            dp[i] -= dp[j];
        }
        ans=(ans+i*dp[i]%MOD)%MOD;
    }
    cout << (ans + MOD) %MOD << '\n';
    return 0;
}