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 = int(input())
  arr = list(map(int, input().split()))
  
  
  if n % 2 == 0:
      tp = sum(arr[::2])
      print(max(sum(arr) - tp, tp))
  elif n == 3:
      print(arr[0] + arr[2])
  else:
      hoge = -(10**12)
      buf = [[hoge for i in range(3)] for j in range(n)]
      buf[0][0] = arr[0]
      buf[1][1] = arr[1]
      buf[2][2] = arr[2]
      buf[2][0] = arr[0] + arr[2]
  
      for i in range(3, n):
          buf[i][0] = buf[i - 2][0] + arr[i]
          buf[i][1] = max(buf[i - 3][0] + arr[i], buf[i - 2][1] + arr[i])
          if i >= 4:
              buf[i][2] = max(
                  [buf[i - 3][1] + arr[i], buf[i - 4][0] + arr[i], buf[i - 2][2] + arr[i]]
              )
          else:
              buf[i][2] = max([buf[i - 3][1] + arr[i], buf[i - 2][2] + arr[i]])
  
      print(max(buf[-1][2], buf[-2][1], buf[-3][0]))
  
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)."}]