1521_E. Nastia and a Beautiful Matrix
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.
```python
def cheak(x):
    return x**2-(x//2)**2>=m and x*(x//2+(1 if x%2!=0 else 0))>=mx
for test in range(int(input())):
    m,k=(int(i) for i in input().split())
    a=[int(i) for i in input().split()]
    mx=max(a)
    z=0;y=m*4
    while z!=y:
        x=(z+y)//2
        if cheak(x):
            y=x
        else:
            z=x+1
    else:
        x=z
    a=sorted(list(map(list,zip(a,range(1,len(a)+1)))))
    def get():
        i=len(a)
        while i!=0:
            i-=1
            while a[i][0]>0:
                a[i][0]-=1
                yield a[i][1] 
        yield 0
    mt=[[0 for i in range(x)] for j in range(x)]
    t=1
    it=get()
    for i in range(0,x,2):
        if t==0:break
        for j in range(1,x,2):
            t=next(it)
            if t:mt[i][j]=t
            else:break
    for i in range(0,x,2):
        if t==0:break
        for j in range(0,x,2):
            t=next(it)
            if t:mt[i][j]=t
            else:break
    for i in range(1,x,2):
        if t==0:break
        for j in range(0,x,2):
            t=next(it)
            if t:mt[i][j]=t
            else:break
    print(len(mt))
    for i in mt:
        print(*i)
```