Yuki has a table with $n$ rows and $m$ columns.

She wants to fill each cell with a non-negative integer no greater than $n \cdot m$ such that the sum of the $\operatorname{mex}^\ast$ of each row and the $\operatorname{mex}$ of each column is maximized.

Formally, let $a_{i,j}$ denote the number in the $i$-th row and $j$-th column of the table. She wants to maximize:

$$ \sum\limits_{i = 1}^{n} \operatorname{mex}\{a_{i,1}, \ldots, a_{i,m}\} + \sum\limits_{j = 1}^{m} \operatorname{mex}\{a_{1,j}, \ldots, a_{n,j}\} $$

Unfortunately, Yuki does not know how to construct this table. Can you help her?

$^\ast$: The $\operatorname{mex}$ of a sequence is the smallest non-negative integer that does not appear in the sequence. For example, $\operatorname{mex}\{0,1,2\}=3$, $\operatorname{mex}\{1,0,3,1\}=2$, and $\operatorname{mex} \varnothing=0$.

Input

This problem contains multiple test cases.

The first line contains a positive integer $t\ (1 \le t \le 10^5)$, representing the number of test cases.

For each test case:

• One line containing two positive integers $n, m\ (1 \le n \cdot m \le 5\cdot10^5)$.

It is guaranteed that the sum of $n \cdot m$ over all test cases does not exceed $5\cdot10^5$.

Output

For each test case, output $n$ lines, each containing $m$ non-negative integers no greater than $n \cdot m$, representing the numbers in your constructed table.

Examples

Input 1

3
2 4
1 1
3 4

Output 1

1 2 0 3
0 3 1 2
0
1 2 0 1
0 1 2 0
2 0 1 3

Note

For the first test case:

• The $\operatorname{mex}$ of the first and second rows of the given table is $4$, the $\operatorname{mex}$ of the first and third columns is $2$, and the $\operatorname{mex}$ of the second and fourth columns is $0$. The sum of the $\operatorname{mex}$ of each row and each column is $12$.
• It can be proven that $12$ is the maximum possible sum of the $\operatorname{mex}$ of each row and each column among all possible constructions.

For the second test case:

• Clearly, $a_{1,1}=0$ maximizes the sum of the $\operatorname{mex}$ of each row and each column.

For the third test case:

• It can be proven that $21$ is the maximum possible sum of the $\operatorname{mex}$ of each row and each column among all possible constructions.