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 = map(int, input().split())
p = 10**9+7
S = 0
memo = []
for i in reversed(range(1, K+1)):
  rep = K//i
  num = pow(rep, N, p)
  sub = 0
  if rep > 1:
    for j in range(rep - 1):
      sub += memo[- i - j * i][1]
  num -= sub
  S += i * num
  S = S%p
  memo += [(i, num)]
print(S)