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 CPP):

Solution:
#include <cstdio>
#include <algorithm>
using namespace std;
#define MAXN 100005
int t, n, m, k;
int a[MAXN];
int order[MAXN];
int tot[MAXN], single[MAXN];
int maxn;

bool cmp(int x, int y)
{
	return a[x] > a[y];
}

void init()
{
	for(int i = 1; i < MAXN; i ++)
	{
		if(i & 1)
		{
			tot[i] = tot[i - 1] + i + i - 1;
			single[i] = single[i - 1] + i + i / 2;
		}else{
			tot[i] = tot[i - 1] + i;
			single[i] = single[i - 1] + i / 2;
		}
		if(single[i] > MAXN)
		{
			maxn = i;
			return;
		}
	}

}

int ans[5005][5005];
int main()
{
	init();
	scanf("%d", &t);
	while(t --)
	{
		scanf("%d%d", &m, &k);
		for(int i = 1; i <= k; i ++) {scanf("%d", a + i); order[i] = i;}
		sort(order + 1, order + k + 1, cmp);
		if(m <= 1)
		{
			printf("1\n%d\n", order[1]);
			continue;
		}	
		int l = 0, r = maxn, mid;
		while(l + 1 < r)
		{
			mid = (l + r) / 2;
			if(tot[mid] >= m && single[mid] >= a[order[1]]) r = mid;
		       	else l = mid;
		}
		int cur, curx = 2, cury = 1, startx = 1, starty = 1;
		for(int i = 1; i <= r; i ++)
			for(int j = 1; j <= r; j ++)
				ans[i][j] = 0;
		for(int i = 1; i <= k; i ++)
		{
			cur = order[i];
			while(a[cur])
			{
				ans[curx][cury] = cur;
				curx += 2;
				if(curx > r)
				{
					curx = starty ^ 3;
					cury += 2;
					if(cury > r)
					{
						curx = startx;
						cury = starty;
						startx = 1;
						starty = 2;
					}
				}
				a[cur] --;
			}
		}
		printf("%d\n", r);
		for(int i = 1; i <= r; i ++)
		{
			for(int j = 1; j <= r; j ++)
			{
				printf("%d ", ans[i][j]);
			}
			putchar('\n');
		}


	}
	return 0;
}