#595 Nostalgia

Statement

Statement language

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 values be . Viewed from the side, row appears to have height . Let the sum of these values be .

Given an integer $X$ , construct any arrangement satisfying $S_1-S_2=X$ . If no such arrangement exists, report that it is impossible.

Input

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

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

Output

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.

Constraints

$1 \leq T \leq 10\,000$ .
$1 \leq N \leq 100$ .
$- 10^{9} \leq X \leq 10^{9}$ .

Subtasks

#	Score	Constraints
1	6	$N \leq 3$ . The sum of $N^2$ over all test cases does not exceed $20$ .
2	12	.

Samples

Input

1
2 1

Output

1 2
3 4

The visible heights of the columns are $3$ and $4$ , while the visible heights of the rows are $2$ and $4$ . Therefore,

S_1=3+4=7,\qquad S_2=2+4=6,