input: Write a python function that computes the number of valid (x, y) pairs such that Alice wins a game played on a circular field surrounded by flowers. Given two integers n and m, where n is the range of clockwise flowers and m is the range of anti-clockwise flowers, the function should ensure that Alice, who takes the first turn, will always win. The function should then return the number of these valid pairs (x, y) according to the following rules:
  
  - In each turn, a player must pick one flower either in the clockwise or anti-clockwise direction.
  - If there are no flowers left at the end of their turn, the current player wins.
  - The number of flowers x in the clockwise direction must be in the range [1, n].
  - The number of flowers y in the anti-clockwise direction must be in the range [1, m].
  
  Constraints: 1 <= n, m <= 10^5
  
  Examples:
  >>> n = 3, m = 2
  3
  >>> n = 1, m = 1
  0
output: def count_valid_pairs(n, m):
      count = 0
      for x in range(1, n + 1):
          for y in range(1, m + 1):
              if (x + y) % 2 == 1:
                  count += 1
      return count