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
ans=0
X=[0]*K
for k in range(1,K+1):
  k=K+1-k
  x=K//k
  if x>1:
    _=pow(x,N,MOD)
    for i in range(x-1):
      _-=X[k*(i+2)-1]
    X[k-1]=_
    ans+=k*_
  else:
    X[k-1]=pow(x,N,MOD)
    ans+=k*X[k-1]
print(ans%MOD)