Nastia and a Beautiful Matrix

题意翻译

你有 $k$ 个数字，他们分别是 $1,2,3,...,k$，对于数字 $i$ 你有相同的 $a_i$ 个。 定义一个 $n\times n$ 的矩阵为美丽矩阵： - 这个 $n\times n$ 的矩阵包含了你所拥有的所有数字； - 对于每个 $2\times 2$ 的子矩阵，占用的格子不能超过 $3$（当一个格子的数为 $0$ 时，我们认为它没有被占用）并且每个对角线的数字是不同的； 现在，你要构造一个最小的美丽矩阵。

题目描述

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.

输入输出格式

输入格式

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 $ .

输出格式

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.

输入输出样例

输入样例 #1

2
3 4
2 0 0 1
15 4
2 4 8 1

输出样例 #1

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

说明

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.