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())
mod=10**9+7
s=[1]*(k+1)
for d in range(1,k//2+1)[::-1]:
  a=pow(k//d,n,mod)
  for i in range(2*d,k+1,d):
    a-=s[i]
  s[d]=a%mod
ans=0
for i,s_i in enumerate(s):
  ans+=i*s_i
  ans%=mod
print(ans)