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:
//#pragma GCC optimize("Ofast,unroll-loops")
#include <bits/stdc++.h>
using namespace std;
typedef long long llo;
#define mp make_pair
#define pb push_back
#define a first 
#define b second
#define endl '\n'
vector<pair<llo,llo>> aa;
vector<llo> cc;

llo m,k;	
llo val[1001][1001];
llo vis[1001];
bool check(llo mid){
	llo coo=0;
	for(llo i=0;i<mid;i++){
		for(llo j=0;j<mid;j++){
			if(vis[i]==1 and vis[j]==1){
				val[i][j]=0;
			}
			else{
				coo++;
				val[i][j]=0;
			}
		}
	}
	if(coo<m){
		return false;
	}
	queue<llo> dd;
	for(auto j:cc){
		dd.push(j);
	}
	
	llo co=0;
	llo co2=0;
	for(llo i=0;i<mid;i++){
		for(llo j=0;j<mid;j++){
			if(vis[i]==0 and vis[j]==1){
				co++;

			}
			else if(vis[i]==1 and vis[j]==0){
				co2++;
			}
		}
	}
	if(co>=co2){
		for(llo i=0;i<mid;i++){
			for(llo j=0;j<mid;j++){
				if(vis[i]==0 and vis[j]==1){
					if(dd.size()){
						val[i][j]=dd.front();
						dd.pop();
					}
				}
				else if(vis[i]==1 and vis[j]==0){
				}
			}
		}
		for(llo i=0;i<mid;i++){
			for(llo j=0;j<mid;j++){
				if(vis[i]==0 and vis[j]==0){
					if(dd.size()){
						val[i][j]=dd.front();
						dd.pop();
					}
				}
			}
		}
		for(llo i=0;i<mid;i++){
			for(llo j=0;j<mid;j++){
				if(vis[i]==0 and vis[j]==1){
					
				}
				else if(vis[i]==1 and vis[j]==0){
					if(dd.size()){
						val[i][j]=dd.front();
						dd.pop();
					}
				}
			}
		}
	}
	else{
		for(llo i=0;i<mid;i++){
			for(llo j=0;j<mid;j++){
				if(vis[i]==0 and vis[j]==1){
					
				}
				else if(vis[i]==1 and vis[j]==0){
					if(dd.size()){
						val[i][j]=dd.front();
						dd.pop();
					}
				}
			}
		}
		for(llo i=0;i<mid;i++){
			for(llo j=0;j<mid;j++){
				if(vis[i]==0 and vis[j]==0){
					if(dd.size()){
						val[i][j]=dd.front();
						dd.pop();
					}
				}
			}
		}
		for(llo i=0;i<mid;i++){
			for(llo j=0;j<mid;j++){
				if(vis[i]%2==0 and vis[j]==1){
					if(dd.size()){
						val[i][j]=dd.front();
						dd.pop();
					}
				}
				else if(vis[i]==1 and vis[j]==0){
				}
			}
		}
	}
	for(llo i=0;i<mid;i++){
		for(llo j=0;j<mid;j++){
			if(i<mid-1 and j<mid-1){
				if(val[i][j]>0 and val[i][j]==val[i+1][j+1]){
					return false;
				}
			}
			if(i>0 and j<mid-1){
				if(val[i][j]>0 and val[i][j]==val[i-1][j+1]){
					return false;
				}
			}
		}
	}
	return true;


}
int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	llo t;
	cin>>t;
	for(llo i=1;i<=1000;i+=2){
		vis[i]=1;
	}
	while(t--){
		
		cin>>m>>k;
		aa.clear();
		cc.clear();
		
		for(llo i=0;i<k;i++){
			llo bb;
			cin>>bb;
			aa.pb({bb,i+1});
		}
		sort(aa.begin(),aa.end());
		reverse(aa.begin(),aa.end());
		for(auto j:aa){
			for(llo i=0;i<j.a;i++){
				cc.pb(j.b);
			}
		}
		llo high=sqrt(2*m)+2;
		for(llo i=19;i>=0;i--){
			if(high-(1<<i)>0){
				if(check(high-(1<<i))){
					high-=(1<<i);
				}
			}
		}
		check(high);
		cout<<high<<endl;
		for(llo i=0;i<high;i++){
			for(llo j=0;j<high;j++){
				cout<<val[i][j]<<" ";
			}
			cout<<endl;
		}


	}








	return 0;
}