Nostalgiabait

In BCD 67, trashmouse mistook this problem for Nostalgia (https://doj.kr/ko/problems/595) and got it wrong. Let us avoid making the same mistake.

There are $N \times N$ buildings arranged in a grid. Let $H_{i,j}$ be the height of the building in row $i$ and column $j$.

All building heights are distinct, and each integer from $1$ through $N^2$ appears exactly once.

When viewed from the front, the visible height of column $j$ is

Let $M_1$ be the minimum of these $N$ values.

When viewed from the side, the visible height of row $i$ is

Let $M_2$ be the minimum of these $N$ values.

An integer $X$ is given. Construct one arrangement of the building heights such that $M_1-M_2=X$. If no such arrangement exists, determine that it is impossible.

The input is given from Standard Input in the following format:

$T$ $\mathrm{case}_1$ $\mathrm{case}_2$ $\vdots$ $\mathrm{case}_T$

Each case is given in the following format:

$N\ X$

For each test case, if no valid arrangement exists, print -1 on one line.

Otherwise, print the matrix $H$ in $N$ lines. On the $i$-th line, print $H_{i,1},H_{i,2},\cdots,H_{i,N}$ separated by spaces.

The printed matrix must contain each of $1,2,\cdots,N^2$ exactly once, and it must satisfy $M_1-M_2=X$ for the values $M_1,M_2$ defined in the statement.

If there are multiple solutions, print any of them.

• $1 \leq T \leq 10\,000$.
• $1 \leq N \leq 100$.
• $-10^9 \leq X \leq 10^9$.
• The sum of $N^2$ over all test cases does not exceed $100\,000$.