3021 - Alice and Bob Playing Flower Game.

Medium

Alice and Bob are playing a turn-based game on a circular field surrounded by flowers. The circle represents the field, and there are x flowers in the clockwise direction between Alice and Bob, and y flowers in the anti-clockwise direction between them.

The game proceeds as follows:

• Alice takes the first turn.

• In each turn, a player must choose either the clockwise or anti-clockwise direction and pick one flower from that side.

• At the end of the turn, if there are no flowers left at all, 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 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].

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

Example 1:

Input: n = 3, m = 2

Output: 3

Explanation: The following pairs satisfy conditions described in the statement: (1,2), (3,2), (2,1).

Example 2:

Input: n = 1, m = 1

Output: 0

Explanation: No pairs satisfy the conditions described in the statement.

Constraints:

• <code>1 <= n, m <= 10⁵</code>