Nostalgia

In Mog's old neighborhood, $N\times N$ buildings are arranged in a grid. Let $H_{i,j}$ be the height of the building in row $i$, column $j$.

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

Viewed from the front, column $j$ appears to have height $\max_{1\leq i\leq N}H_{i,j}$. Let the sum of these $N$ values be $S_1$. Viewed from the side, row $i$ appears to have height $\max_{1\leq j\leq N}H_{i,j}$. Let the sum of these values be $S_2$.

Given an integer $X$, construct any arrangement satisfying $S_1-S_2=X$. If no such arrangement exists, report 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. The $i$-th line must contain $H_{i,1},H_{i,2},\cdots,H_{i,N}$ separated by spaces.

If multiple arrangements are possible, 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 $100\,000$.