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: from itertools import combinations
  
  
  def gcd(x, y):
      if y == 0:
          return x
      return gcd(y, x % y)
  
  
  def gcdn(l: list):
      if len(l) == 2:
          return gcd(*l)
      g = gcd(l[0], l[1])
      for li in l[2:]:
          g = gcd(g, li)
      return g
  
  
  n, k = map(int, input().split())
  
  comb = list(combinations(range(1, k + 1), n))
  print(comb)
  
  cnt = 0
  for l in comb:
      unq = len(list(set(l)))
      cnt += (gcdn(l) * k ** (unq - 1)) % (10**9 + 7)
  print(cnt)
  
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)."}]