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()))
S = 0
out = [0]*(K+1)
p = 10**9+7
for i in range(K):
    X = K-i
    out[X] = pow(int(K/X),N,p)
    t=2
    while t*X<=K:
        out[X] = out[X]-out[t*X]
        t+=1
    S = (S + X*out[X])%p
print(S)