Problem: 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 ≤ i ≤ k) you have.

An n × n matrix is called beautiful if it contains all the numbers you have, and for each 2 × 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 ≤ t ≤ 10 000) — the number of test cases.

The first line of each test case contains 2 integers m and k (1 ≤ m, k ≤ 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, …, a_{k} (0 ≤ a_i ≤ m, a_1 + a_2 + … + 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 ⋅ 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 ≤ b_{i, j} ≤ 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.

Solution (in PYTHON3):

Solution:
from math import sqrt, ceil
for iter in range(int(input())):
    m, k = map(int, input().split());A = list(map(int, input().split()));A = sorted(list(enumerate(A)), reverse=True, key=lambda x: x[1]);B = [];C = []
    for elem in A:
        if len(B) > len(C):            C += [elem[0] + 1] * elem[1]
        else:            B += [elem[0] + 1] * elem[1]
    if len(C) > len(B):C, B = B, C
    even_n = ceil(max(sqrt(4 * m / 3), sqrt(2 * len(B))))
    if even_n % 2 == 1:
        even_n += 1
    odd_n = even_n - 1
    if odd_n ** 2 - (odd_n - 1) ** 2 / 4 >= m and odd_n * (odd_n + 1) / 2 >= len(B):
        n = odd_n
    else:
        n = even_n
    if n % 2 == 0:
        C += [0] * (3 * n ** 2 // 4 - len(B) - len(C))
    else:
        C += [0] * (n ** 2 - (n - 1) ** 2 // 4 - len(B) - len(C))
    if n % 2 == 0:
        border = n ** 2 // 4
    else:
        border = (n - 1) * (n + 1) // 4
    B, D = B[:border], B[border:]
    D += C[border:]
    C = C[:border]
    B_cnt = 0
    C_cnt = 0
    D_cnt = 0
    print(n)
    for i in range(n):
        for j in range(n):
            if i % 2 == 1 and j % 2 == 1:                print(0, end=' ')
            elif i % 2 == 1:print(B[B_cnt], end=' ');B_cnt += 1
            elif j % 2 == 1:print(C[C_cnt], end=' ');C_cnt += 1
            else:print(D[D_cnt], end=' ');D_cnt += 1
        print()