output_description: Print the sum of \gcd(A_1, ..., A_N) over all K^N sequences, modulo (10^9+7).
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N K
attempt: 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)
  
problem_description: Statement
  
  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.
samples: [{"input": "3 2", "output": "9\n    \n\n\\gcd(1,1,1)+\\gcd(1,1,2)+\\gcd(1,2,1)+\\gcd(1,2,2)\n+\\gcd(2,1,1)+\\gcd(2,1,2)+\\gcd(2,2,1)+\\gcd(2,2,2) =1+1+1+1+1+1+1+2=9\n\nThus, the answer is 9.\n\n* * *"}, {"input": "3 200", "output": "10813692\n    \n\n* * *"}, {"input": "100000 100000", "output": "742202979\n    \n\nBe sure to print the sum modulo (10^9+7)."}]