OSN 2021 Problem 8

On a $100 \times 100$ chessboard, the plan is to place several $1 \times 3$ boards and $3 \times 1$ board, so that

• Each tile of the initial chessboard is covered by at most one small board.
• The boards cover the entire chessboard tile, except for one tile.
• The sides of the board are placed parallel to the chessboard.

Suppose that to carry out the instructions above, it takes $H$ number of $1 \times 3$ boards and $V$ number of $3 \times 1$ boards. Determine all possible pairs of $(H,V)$ .

Proposed by Muhammad Afifurrahman, Indonesia