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<iostream>
#include<cstdio>
#include<algorithm>
#include<vector>
using namespace std;
vector<pair<int,int> >aa;
int a[1005][1005];
int main()
{
	int t;
	scanf("%d",&t);
	while(t--)
	{
		int m,k;
		scanf("%d%d",&m,&k);
		aa.clear();
		for(int i=1;i<=k;i++)
		{
			int x;scanf("%d",&x);
			aa.push_back(make_pair(x,i));
		}
		sort(aa.begin(),aa.end());
		reverse(aa.begin(),aa.end());
		int n=0;
		
		while(n*n-(n/2)*(n/2)<m||n*((n+1)/2)<aa[0].first)
		n++;
	//	for(int i=0;i<k;i++)
	//	cout<<aa[i].first<<" "<<aa[i].second<<endl;
		printf("%d\n",n);
		aa.push_back(make_pair(1e9,0));
		int now=0;
		for(int i=1;i<=n;i+=2)
		for(int j=2;j<=n;j+=2)
		{
			a[i][j]=aa[now].second;
		//	cout<<i<<" "<<j<<" "<<aa[now].second<<endl;
			aa[now].first--;
			while(aa[now].first==0)
			now++;
		}
		for(int i=1;i<=n;i+=2)
		for(int j=1;j<=n;j+=2)
		{
			a[i][j]=aa[now].second;
		//	cout<<i<<" "<<j<<" "<<aa[now].second<<endl;
			aa[now].first--;
			while(aa[now].first==0)
			now++;
		}
		for(int i=2;i<=n;i+=2)
		for(int j=1;j<=n;j+=2)
		{
			a[i][j]=aa[now].second;
		//	cout<<i<<" "<<j<<" "<<aa[now].second<<endl;
			aa[now].first--;
			while(aa[now].first==0)
			now++;
		}
		for(int i=1;i<=n;i++,puts(""))
		for(int j=1;j<=n;j++)
		printf("%d ",a[i][j]);
	}
}