Rubik's Rectangle

A new puzzle mixes Rubik's Cube with the Fifteen puzzle. The board is an $H \times W$ frame packed with tiles, and the numbers $1$ through $H \times W$ each appear on exactly one tile.

The only allowed move is flipping one whole row or one whole column. A flip reverses the order of the tiles in that row (or in that column). Flipping row 3, for example, reverses the order of the tiles in row 3 and moves nothing else.

The board is sorted when the cell in row $i$ and column $j$ holds $(i-1) \times W + j$. Given a board whose tiles lie in an arbitrary order, decide whether repeated flips can bring it to the sorted position.

The first line contains the number of test cases $T$. The test cases follow.

Each test case starts with an empty line. The next line contains two space-separated integers $W$ and $H$ ($1 \le W, H \le 100$), the width and the height of the puzzle. Each of the next $H$ lines contains $W$ space-separated integers, the numbers printed on that row's tiles from left to right.

Print the answers to the test cases in the order in which they appear in the input, one per line. Print POSSIBLE if the puzzle can be brought to the sorted position, and IMPOSSIBLE if it cannot.