E. Nastia and a Beautiful Matrix
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You like numbers, don't you? Nastia has a lot of numbers and she wants to share them with you! Isn't it amazing?

Let $$$a_i$$$ be how many numbers $$$i$$$ ($$$1 \le i \le k$$$) you have.

An $$$n \times n$$$ matrix is called beautiful if it contains all the numbers you have, and for each $$$2 \times 2$$$ submatrix of the original matrix is satisfied:

  1. The number of occupied cells doesn't exceed $$$3$$$;
  2. The numbers on each diagonal are distinct.

Make a beautiful matrix of minimum size.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10\,000$$$) — the number of test cases.

The first line of each test case contains $$$2$$$ integers $$$m$$$ and $$$k$$$ ($$$1 \le m, k \le 10^5$$$) — how many numbers Nastia gave you and the length of the array $$$a$$$, respectively.

The second line of each test case contains $$$k$$$ integers $$$a_1, a_2, \ldots, a_{k}$$$ ($$$0 \le a_i \le m$$$, $$$a_1 + a_2 + \ldots + a_{k} = m$$$), where $$$a_i$$$ is how many numbers $$$i$$$ you have.

It's guaranteed that the sum of $$$m$$$ and $$$k$$$ in one test doesn't exceed $$$2 \cdot 10^5$$$.

Output

For each $$$t$$$ test case print a single integer $$$n$$$ — the size of the beautiful matrix.

In the next $$$n$$$ lines print $$$n$$$ integers $$$b_{i, j}$$$ ($$$0 \le b_{i, j} \le k$$$; if position is empty, print $$$b_{i, j} = 0$$$) — the beautiful matrix $$$b$$$ you made up.

Example
Input
2
3 4
2 0 0 1
15 4
2 4 8 1
Output
2
4 1
0 1
5
3 0 0 2 2
3 2 3 3 0
0 1 0 4 0
3 0 0 0 0
2 1 3 3 3
Note

Note that $$$0$$$ in this problem represents a blank, not a number.

Examples of possible answers for the first test case:

$$$\begin{array}{cc} 1 & 1 \\ 4 & 0 \\ \end{array} \hspace{0,5cm} \begin{array}{cc} 1 & 4 \\ 1 & 0 \\ \end{array} \hspace{0,5cm} \begin{array}{cc} 4 & 0 \\ 1 & 1 \\ \end{array}$$$

Examples of not beautiful matrices for the first test case:

$$$\begin{array}{cc} 1 & 0 \\ 4 & 1 \\ \end{array} \hspace{0,5cm} \begin{array}{cc} 4 & 1 \\ 7 & 1 \\ \end{array} \hspace{0,5cm} \begin{array}{cc} 1 & 0 \\ 4 & 0 \\ \end{array}$$$

The example of the not beautiful matrix for the second test case:

$$$\begin{array}{cc} 3 & 4 & 0 & 2 & 2 \\ 3 & 2 & 3 & 3 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 3 & 0 & 0 & 0 & 0 \\ 2 & 1 & 3 & 3 & 3 \\ \end{array}$$$

Everything is okay, except the left-top submatrix contains $$$4$$$ numbers.