Alice and Bob Playing Flower Game
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Description
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 lane 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, the task is to compute the number of possible pairs (x, y) that satisfy the 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.
Example 1:
Example 2:
Solution