#214209. [ZJCPC 2017] Domino Tiling

Chiaki has an rectangular chessboard. She would like to tile this board with dominoes, where a domino is a rectangle, such that:

• all the squares of the board are covered but no dominoes overlap or lie partially off the board.
• there must be no points where corners of four different dominoes meet.

The figure below shows some forbidden configurations:

:::align{center} :::

The figure below shows two valid tilings of chessboard:

:::align{center} :::

You also need to number the dominoes of chessboard so that no two dominoes have the same number. You can use the number from to .

There are multiple test cases. The first line of input contains an integer , indicating the number of test cases. For each test case:

The first line contains two integers and -- the size of the rectangular chessboard.

It is guaranteed that the sum of over all test cases does not exceed .

For each test case, output a valid chessboard described above. A valid chessboard consists of lines and each line contains integers. Each integer in the output should represent the of a domino. The grids sharing the same belong to the same domino.

If there is no solution, output "Impossible!"" (without the quotes) instead.

样例输入 1

3
1 1
4 3
4 4

样例输出 1

Impossible!
1 2 2 
1 3 3 
5 5 4 
6 6 4 
1 1 3 3 
5 7 7 6 
5 8 8 6 
2 2 4 4