E. Nastia and a Beautiful Matrixtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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:   The number of occupied cells doesn't exceed 3;  The numbers on each diagonal are distinct. Make a beautiful matrix of minimum size.InputThe 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.OutputFor 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. ExampleInput
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 3NoteNote 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.
2
3 4
2 0 0 1
15 4
2 4 8 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
['binary search', 'constructive algorithms', 'dp', 'greedy', '*2700']