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;

#define LL long long
#define mod 1000000007

LL n, k, ans;

LL power(LL x, LL y) { 
    LL res = 1;
    x = x % mod;

    while (y > 0) { 
        if (y & 1) 
            res = (res*x) % mod; 
        y = y>>1;
        x = (x*x) % mod; 
    } 
    return res; 
} 

int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);

    cin >> n >> k;
    LL dp[k + 1];

    for(int i = k; i > 0; i--) {
    	dp[i] = power(k / i, n);
    	for(int j = i + i; j <= k; j += i) dp[i] -= dp[j];
    	ans = (ans + (1LL * i * dp[i]) % mod) % mod;
    }
    cout << (ans + mod) % mod;
}