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 = int(1e9+7)
A = [0] * (K+1)
ans = 0

for i in range(K,0,-1):
  #print(i, K//i, N, mod)
  A[i] = pow(K//i, N, mod)
  idx = 2*i
  while idx <= K:
    A[i] = (A[i] - A[idx]) % mod
    idx += i
  ans = (ans + A[i] * i) % mod
print(ans)
