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
N,K = list(map(int,input().split()))

MOD = 10**9+7
arr = [pow(K//i, N, MOD) for i in range(1,K+1)]

for i in range(K//2,0,-1):
    arr[i-1] -= sum(arr[2*i-1:K:i]) % MOD
    arr[i-1] %= MOD
    
arr = [(i+1)*j%MOD for i,j in enumerate(arr)]

print(sum(arr)%MOD)