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
Big=10**9+7
_=list(map(int,input().split(" ")))
N=_[0]
K=_[1]
gcd_list=[0 for _ in range(K)]
for i in range(K):
  s=K-i-1
  gcd_list[s]=(pow(K//(K-i), N, Big)-(sum(gcd_list[2*s+1::s+1]))%Big)%Big
answer=[(x+1)*gcd_list[x]%Big for x in range(K)]
print(sum(answer)%Big)