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 JAVA):

Solution:
import java.io.*;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.util.List;
 import java.util.*;
 public class realfast implements Runnable 
  {
    private static final int INF = (int) 1e9;
    long in= 1000000007;
    long fac[]= new long[1000001];
    long inv[]=new long[1000001];
    public  void solve() throws IOException 
    {

        //int t = readInt();
        int t = readInt();

        for(int f =0;f<t;f++)
        {
             int m = readInt();
             int k = readInt();
             ArrayList<edge> arr= new ArrayList<edge>();

             for(int i=1;i<=k;i++)
             {
                 int a = readInt();
                 if(a>0)
                 arr.add(new edge(i,a));
             }

             Collections.sort(arr);
             int n=1;
             int pal =0;
             for(int i=1;i<=m;i++)
             {
                 int c= i*((i+1)/2);
                 
                 pal= pal+2*i-1;
                 if(i%2==0)
                 {
                    pal=pal-i+1;
                 }
                  int v = arr.get(arr.size()-1).v;

                  if(v<=c&&m<=pal)
                  {
                         n=i;
                         break;
                  }
             }

             int mat[][]=new int[n+1][n+1];

             int odd = n*((n+1)/2);
             
             
             ArrayList<Integer> o = new ArrayList<Integer>();
             ArrayList<Integer> e= new ArrayList<Integer>();
             int count =0;
             for(int i=arr.size()-1;i>=0;i--)
             {
                int u = arr.get(i).u;
                int v = arr.get(i).v;

                while(v>0)
                {
                    count++;
                    if(count<=odd)
                        o.add(u);
                    else
                        e.add(u);
                    v--;
                }

             }
          //   out.println(o.size()+" "+e.size());
             int start =o.size()-1;
             for(int i=1;i<=n;i=i+2)
             {
                if(start<0)
                           break;
                for(int j=1;j<=n;j=j+2)
                {
                      
                      if(start<0)
                           break;

                      mat[i][j]= o.get(start);
                  //     out.print(mat[i][j]+" ");
                      start--;
                }
             }
             for(int i=1;i<=n;i=i+2)
             {
                if(start<0)
                           break;
                for(int j=2;j<=n;j=j+2)
                {
                      
                      if(start<0)
                           break;

                      mat[i][j]= o.get(start);
                  //     out.print(mat[i][j]+" ");
                      start--;
                }
             }
             start=e.size()-1;
             for(int i=2;i<=n;i=i+2)
             {
                if(start<0)
                           break;
                for(int j=1;j<=n;j=j+2)
                {
                      
                      if(start<0)
                           break;

                      mat[i][j]= e.get(start);
                      start--;
                    //  out.print(mat[i][j]+" ");
                }
             }
           //  out.println();
             out.println(n);

             for(int i=1;i<=n;i++)
             {
                for(int j=1;j<=n;j++)
                {
                    out.print(mat[i][j]+" ");
                }
                out.println();
             }



        }
       

    }
    
    public int value (int seg[], int left , int right ,int index, int l, int r)
    {
            
            if(left>right)
            {
              return -100000000;
            }
            if(right<l||left>r)
                return -100000000;
            if(left>=l&&right<=r)
                return seg[index];
            int mid = left+(right-left)/2;
            int val = value(seg,left,mid,2*index+1,l,r);
            int val2 = value(seg,mid+1,right,2*index+2,l,r);
            return Math.max(val,val2);

    }
   
    public int gcd(int a , int b )
    {
      if(a<b)
      {
        int t =a;
        a=b;
        b=t;
      }
      if(a%b==0)
        return b ;
      return gcd(b,a%b);
    }
    public long pow(long n , long p,long m)
    {
         if(p==0)
            return 1;
        long val = pow(n,p/2,m);;
        val= (val*val)%m;
        if(p%2==0)
            return val;
        else
            return (val*n)%m;
    }
    
    
    ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////
    public static void main(String[] args) {
        new Thread(null, new realfast(), "", 128 * (1L << 20)).start();
    }
 
    private static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
    private BufferedReader reader;
    private StringTokenizer tokenizer;
    private PrintWriter out;
 
    @Override
    public void run() {
        try {
            if (ONLINE_JUDGE || !new File("input.txt").exists()) {
                reader = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
            } else {
                reader = new BufferedReader(new FileReader("input.txt"));
                out = new PrintWriter("output.txt");
            }
            solve();
        } catch (IOException e) {
            throw new RuntimeException(e);
        } finally {
            try {
                reader.close();
            } catch (IOException e) {
                // nothing
            }
            out.close();
        }
    }
 
    private String readString() throws IOException {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }
 
    @SuppressWarnings("unused")
    private int readInt() throws IOException {
        return Integer.parseInt(readString());
    }
 
    @SuppressWarnings("unused")
    private long readLong() throws IOException {
        return Long.parseLong(readString());
    }
 
    @SuppressWarnings("unused")
    private double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }
}
class edge implements Comparable<edge>{
    int u ;
    int v;
    
    edge(int u, int v)
    {
       this.u=u;
       this.v=v;
    }
    public int compareTo(edge e)
    {
        return this.v-e.v;
    }
}