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>
#define N 3005
#define M 300005
using namespace std;
int m,k,a[M],cnt,c[N][N];
pair<int,int> b[M];
vector<pair<int,int> >p,q,w;
void calc(int n){
	p.clear();q.clear();w.clear();
	for(int i=0;i<=n+1;i++)	
		for(int j=0;j<=n+1;j++)	
			c[i][j]=0;
	for(int i=1;i<=n;i++)
		for(int j=1;j<=n;j++)
			if(i&1){
				if(j&1)w.push_back(make_pair(i,j));
				else p.push_back(make_pair(i,j));
			}
			else 
				if(j&1)q.push_back(make_pair(i,j));
	for(int i=cnt;i>=1;i--){
		for(int j=1;j<=b[i].first;j++){
			if(p.size()){
				pair<int,int> now=p[p.size()-1];
				p.pop_back();
				c[now.first][now.second]=b[i].second; 
			}
			else {
				if(q.size()){
					pair<int,int> now=q[q.size()-1];
					int x=now.first,y=now.second,col=b[i].second;
					if(c[x-1][y-1]!=col&&c[x-1][y+1]!=col&&c[x+1][y-1]!=col&&c[x+1][y+1]!=col){
						c[x][y]=col;q.pop_back();
					}
					else{
						now=w[w.size()-1];
						c[now.first][now.second]=col;w.pop_back();
					}
				}
				else{
					pair<int,int> now=w[w.size()-1];
					c[now.first][now.second]=b[i].second;w.pop_back();
				}
			}
		}
	}
	for(int i=1;i<=n;i++){
		for(int j=1;j<=n;j++)
			printf("%d ",c[i][j]);
		printf("\n");
	}
}
void solve(){
	scanf("%d%d",&m,&k);cnt=0;
	for(int i=1;i<=k;i++){
		scanf("%d",&a[i]);
		if(a[i])b[++cnt]=make_pair(a[i],i);
	}
	sort(b+1,b+cnt+1);
	int l=1,r=3000,ans=0;
	while(l<=r){
		int mid=(l+r)/2;
		if(mid*((mid+1)/2)>=b[cnt].first && ((mid*mid)-(mid/2)*(mid/2))>=m)
			ans=mid,r=mid-1;
		else 
			l=mid+1;
	}
	printf("%d\n",ans);calc(ans);
}
int main(){
	int t;
	scanf("%d",&t);
	while(t--)solve();
	return 0;
}