Alice and Bob Playing Flower Game

Alice and Bob are playing a turn-based game on a field, with two lanes of flowers between them. There are x flowers in the first lane between Alice and Bob, and y flowers in the second lane between them.

The game proceeds as follows:

• Alice takes the first turn.
• In each turn, a player must choose either one of the lanes and pick one flower from that side.
• At the end of the turn, if there are no flowers left at all in either lane, the current player captures their opponent and wins the game.

Given two integers, n and m, compute the number of possible pairs (x, y) that satisfy these conditions:

• Alice must win the game according to the described rules.
• The number of flowers x in the first lane must be in the range [1, n].
• The number of flowers y in the second lane must be in the range [1, m].

Return the number of possible pairs (x, y) that satisfy the conditions mentioned in the statement.