Knight's Tour Challenge

Consider a standard chessboard of size \(n \times n\). A knight is placed at the initial position \((x, y)\) and is allowed to make at most \(k\) moves. The knight moves in an 'L' shape: two squares in one direction and then one square perpendicular to that.

Your task is to determine whether the knight can visit every square on the board (i.e. all \(n^2\) squares) within \(k\) moves. If it is possible, print possible; otherwise, print impossible.

inputFormat

The input is read from standard input and consists of four space-separated integers:

• n: the size of the chessboard (the board is \(n \times n\)).
• k: the maximum number of moves allowed.
• x: the starting x-coordinate (row index, 1-indexed).
• y: the starting y-coordinate (column index, 1-indexed).

outputFormat

The output is a single line printed to standard output. It should be possible if the knight can visit every square within \(k\) moves, and impossible otherwise.

## sample

5 32 1 1

possible

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