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=int(1e9)+7

dp=[0]*(K+1)
for i in range(K):
  j=K-i
  dp[j]+=pow(K//j, N, MOD)

  k=2*j
  while k<=K:
    dp[j]=(dp[j]-dp[k]+MOD) % MOD
    k+=j

ans=0
for i in range(1,K+1):
  ans+=dp[i]*i
  ans%=MOD
print(ans)