output_description: Print the sum of the costs of all possible arrangements of the pieces, modulo
  10^9+7.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N M K
attempt: p, q, r = map(int, input().split())
  
  
  def comb_mod(N, K, modp):
  
      K_fact = 1
      NK_fact = 1
      N_fact = 1
  
      for i in range(1, K + 1):
          K_fact *= i
          K_fact = K_fact % modp
      for i in range(1, N - K + 1):
          NK_fact *= i
          NK_fact = NK_fact % modp
      for i in range(1, N + 1):
          N_fact *= i
          N_fact = N_fact % modp
  
      K_inv = pow(K_fact, -1, modp)
      NK_inv = pow(NK_fact, -1, modp)
      pat = (N_fact * K_inv) % modp * NK_inv % modp
      return pat
  
  
  pat = comb_mod(p * q - 2, r - 2, 10**9 + 7)
  
  ans = 0
  for i in range(0, q + 1):
      ans += i * (q - i) * p * p
      ans = ans % (10**9 + 7)
  
  for k in range(0, p + 1):
      ans += k * (p - k) * q * q % (10**9 + 7)
      ans = ans % (10**9 + 7)
  
  print(ans * pat % (10**9 + 7))
  
problem_description: Statement
  
  We have a grid of squares with N rows and M columns. Let (i, j) denote the
  square at the i-th row from the top and j-th column from the left. We will
  choose K of the squares and put a piece on each of them.
  
  If we place the K pieces on squares (x_1, y_1), (x_2, y_2), ..., and (x_K,
  y_K), the _cost_ of this arrangement is computed as:
  
  \sum_{i=1}^{K-1} \sum_{j=i+1}^K (|x_i - x_j| + |y_i - y_j|)
  
  Find the sum of the costs of all possible arrangements of the pieces. Since
  this value can be tremendous, print it modulo 10^9+7.
  
  We consider two arrangements of the pieces different if and only if there is a
  square that contains a piece in one of the arrangements but not in the other.
samples: [{"input": "2 2 2", "output": "8\n    \n\nThere are six possible arrangements of the pieces, as follows:\n\n  * ((1,1),(1,2)), with the cost |1-1|+|1-2| = 1\n  * ((1,1),(2,1)), with the cost |1-2|+|1-1| = 1\n  * ((1,1),(2,2)), with the cost |1-2|+|1-2| = 2\n  * ((1,2),(2,1)), with the cost |1-2|+|2-1| = 2\n  * ((1,2),(2,2)), with the cost |1-2|+|2-2| = 1\n  * ((2,1),(2,2)), with the cost |2-2|+|1-2| = 1\n\nThe sum of these costs is 8.\n\n* * *"}, {"input": "4 5 4", "output": "87210\n    \n\n* * *"}, {"input": "100 100 5000", "output": "817260251\n    \n\nBe sure to print the sum modulo 10^9+7."}]