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: mod = 10**9 + 7
  N, K = map(int, input().split())
  Ans = [1 for k in range(K)]
  c = K
  for j in range(N):
      Ans[0] = Ans[0] * (K) % mod
  for k in range(2, (K + 1) // 2 + 1):
      d = K // k
      if c == d:
          Ans[k - 1] = Ans[k - 2]
      else:
          for j in range(N):
              Ans[k - 1] = Ans[k - 1] * d % mod
          c = d
  print(Ans)
  for j in range(K, 1, -1):
      for l in range(j // 2, 0, -1):
          if j % l == 0:
              Ans[l - 1] -= Ans[j - 1]
  for j in range(K):
      Ans[j] *= j + 1
  print(sum(Ans) % mod)
  
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)."}]