output_description: Print the sum of the scores, modulo 10^9 + 7.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      H W K
attempt: h, w, k = map(int, input().split())
  p, n = 10**9 + 7, h + w
  x = (
      k
      + k * (k + 1) // 2
      + k * (k - 1) * (k + 1) // 3 * h * w * pow(n * (n - 1), p - 2, p)
  )
  for i in range(n, n - k, -1):
      x = x * i % p
  print(x)
  
problem_description: Statement
  
  There is a rectangular sheet of paper with height H+1 and width W+1. We
  introduce an xy-coordinate system so that the four corners of the sheet are
  (0, 0), (W + 1, 0), (0, H + 1) and (W + 1, H + 1).
  
  This sheet can be cut along the lines x = 1,2,...,W and the lines y =
  1,2,...,H. Consider a sequence of operations of length K where we choose K of
  these H + W lines and cut the sheet along those lines one by one in some
  order.
  
  Let the score of a cut be the number of pieces of paper that exist just after
  the cut. The score of a sequence of operations is the sum of the scores of all
  of the K cuts.
  
  Find the sum of the scores of all possible sequences of operations of length
  K. Since this value can be extremely large, print the number modulo 10^9 + 7.
samples: [{"input": "2 1 2", "output": "34\n    \n\nLet x_1, y_1 and y_2 denote the cuts along the lines x = 1, y = 1 and y = 2,\nrespectively. The six possible sequences of operations and the score of each\nof them are as follows:\n\n  * y_1, y_2: 2 + 3 = 5\n  * y_2, y_1: 2 + 3 = 5\n  * y_1, x_1: 2 + 4 = 6\n  * y_2, x_1: 2 + 4 = 6\n  * x_1, y_1: 2 + 4 = 6\n  * x_1, y_2: 2 + 4 = 6\n\nThe sum of these is 34.\n\n* * *"}, {"input": "30 40 50", "output": "616365902\n    \n\nBe sure to print the sum modulo 10^9 + 7."}]