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;
#define LL long long
#define pa pair<int,int>
const int N=100010;
const int inf=2147483647;
LL read()
{
	LL x=0,f=1;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9')x=x*10ll+ch-'0',ch=getchar();
	return x*f;
}
int s,n,b[N],a[1000][1000];
struct P
{
	int x,v;
}p[N];
bool cmp(P a,P b){return a.v>b.v;}
int D;
bool check(int x,int y,int z)
{
	if(y>1&&a[x-1][y-1]==z)return false;
	if(y<D&&a[x-1][y+1]==z)return false;
	if(y>1&&x<D&&a[x+1][y-1]==z)return false;
	if(y<D&&x<D&&a[x+1][y+1]==z)return false;
	if(y>1&&a[x][y-1])return false;
	return true;
}
int main()
{
	int T=read();
	while(T--)
	{
		s=read(),n=read();int mx=0;
		for(int i=1;i<=n;i++)p[i].x=i,p[i].v=read(),mx=max(mx,p[i].v);
		sort(p+1,p+1+n,cmp);
		int u=0;
		for(int i=1;i<=n;i++)
		for(int j=1;j<=p[i].v;j++)
		b[++u]=p[i].x;
		for(int d=1;;d++)
		{
			int n1=(d+1)/2*d,n2=(d/2)*((d+1)/2);
			if(n1>=mx&&n1+n2>=s)
			{
				D=d;
				cout<<d<<endl;
				for(int i=1;i<=d;i++)
				for(int j=1;j<=d;j++)
				a[i][j]=0;
				int t=0;
				if(n1>=s)
				{
					for(int i=1;i<=d;i+=2)
					for(int j=1;j<=d;j++)
					if((++t)<=s)a[i][j]=b[t];
					for(int i=1;i<=d;i++)
					{
						for(int j=1;j<=d;j++)
						printf("%d ",a[i][j]);
						puts("");
					}
					break;
				}
				if(n1==mx)
				{
					for(int i=1;i<=d;i+=2)
					for(int j=1;j<=d;j++)
					if((++t)<=s)a[i][j]=b[t];
				}
				else
				{
					int cnt=1;
					for(int i=n1-1;i;i--)
					if(b[i]==b[i+1])cnt++;
					else break;
					for(int i=1;i<=d;i+=2)
					for(int j=1;j<=d;j+=2)
					if(cnt)cnt--,a[i][j]=b[n1];
					for(int i=1;i<=d;i+=2)
					for(int j=1;j<=d;j++)
					if(!a[i][j])a[i][j]=b[++t];
				}
				t=n1+1;
//				cout<<b[t]<<endl;
				for(int i=2;i<=d;i+=2)
				for(int j=1;j<=d;j++)
				if(t<=s&&check(i,j,b[t]))a[i][j]=b[t++];
				for(int i=1;i<=d;i++)
				{
					for(int j=1;j<=d;j++)
					printf("%d ",a[i][j]);
					puts("");
				}
				break;
			}
		}
	}
}