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: n, k = map(int, input().split())
  
  count_list = [0 for _ in range(k)]
  for num in reversed(range(1, k + 1)):
      # count = (k//num)**n
      count = pow(k // num, n, 1000000007)
      count_list[num - 1] = count
  
  for num in reversed(range(1, k + 1)):
      if k // num >= 2:
          for i in range(2, k // num + 1):
              count_list[num - 1] -= count_list[num * i - 1]
  
  score = 0
  for idx, val in enumerate(count_list):
      score += (idx + 1) * val
  
  print(score % 1000000007)
  
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)."}]