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<algorithm>
#include<cstdio>
#include<cmath>
using namespace std;
typedef long long ll;
ll t,m,k,n;
struct node{
	ll num,sum;
}a[100005];
bool cmp(node x,node y){
	return x.sum>y.sum;
}
ll f[805][805];
int main(){
	scanf("%lld",&t);
	while(t--){
		scanf("%lld%lld",&m,&k);
		for(int i=1;i<=k;i++){
			scanf("%lld",&a[i].sum);
			a[i].num=i;
		}
		sort(a+1,a+1+k,cmp);
		for(int i=(int)(sqrt(m));;i++){
			if(m<=i*i-(ll)(i/2)*(ll)(i/2)&&a[1].sum<=i*(ll)((i+1)/2)){
				n=i;
				break;
			}
		}
		for(int i=1;i<=n;i++)
			for(int j=1;j<=n;j++)
				f[i][j]=0;
		ll b=1;
		for(int i=1;i<=n;i+=2){
			for(int j=2;j<=n;j+=2){
				f[i][j]=a[b].num;
				a[b].sum--;
				while(a[b].sum==0) b++;
				if(b>k) break;
			}
			if(b>k) break;
 		}
 		for(int i=1;i<=n;i+=2){
			for(int j=1;j<=n;j+=2){
				f[i][j]=a[b].num;
				a[b].sum--;
				while(a[b].sum==0) b++;
				if(b>k) break;
			}
			if(b>k) break;
 		}
 		if(b<=k){
 			for(int i=2;i<=n;i+=2){
 				for(int j=1;j<=n;j+=2){
 					f[i][j]=a[b].num;
					a[b].sum--;
					while(a[b].sum==0) b++;
					if(b>k) break;
				 }
				 if(b>k) break;
			 }
		}
		printf("%lld\n",n);
		for(int i=1;i<=n;i++,printf("\n"))
			for(int j=1;j<=n;j++)
				printf("%lld ",f[i][j]);
	}
	return 0;
}