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<bits/stdc++.h>
using namespace std;
const int M=998244353;
const int N=1005,E=524288;
int t,n,as[N][N],m,a[N*N],id[N*N],l,i,j;
bool cmp(int x,int y)
{
	return a[x]>a[y];
}
int Nex()
{
	while(l<=n&&!a[id[l]])
		++l;
	--a[id[l]];
	return id[l];
}
int main()
{
	scanf("%d",&t);
	while(t--)
	{
		scanf("%d %d",&m,&n);
		int mx=0;
		for(i=1;i<=n;++i)
		{
			scanf("%d",&a[i]);
			id[i]=i;
			mx=max(mx,a[i]);
		}
		sort(id+1,id+1+n,cmp);
		id[n+1]=0;
		for(i=1;;++i)
			if(i*((i+1)/2)>=mx&&(i/2)*(i/2)*3+(i&1)*(2*i-1)>=m)
				break;
		int p=i;
		l=1;
		for(i=1;i<=p;i+=2)
			for(j=2;j<=p;j+=2)
				as[i][j]=Nex();
		for(i=1;i<=p;i+=2)
			for(j=1;j<=p;j+=2)
				as[i][j]=Nex();
		for(i=2;i<=p;i+=2)
			for(j=1;j<=p;j+=2)
				as[i][j]=Nex();
		printf("%d\n",p);
		for(i=1;i<=p;++i)
		{
			for(j=1;j<=p;++j)
				printf("%d ",as[i][j]);
			printf("\n");
		}
	}
}