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.util.*;
import java.io.*;

public class E
{

	static FastIO f;

	public static void main(String args[]) throws IOException
	{
		f = new FastIO();

		int t, m, k, n, i, j, x;
		Pair[] a;
		int[][] ans;
		
		t = f.ni();
		
		while(t-->0)
		{
			m = f.ni();
			k = f.ni();
			a = new Pair[k];

			for(i = 0, j = 0; i < k; i++)
			{
				x = f.ni();
				j = Math.max(j, x);
				a[i] = new Pair(i+1, x);
			}

			Arrays.sort(a, new Comparator<Pair>(){

				@Override
				public int compare(Pair a, Pair b)
				{
					return b.f - a.f;
				}
			});

			// f.err(Arrays.toString(a) + "\n");

			for(n = 1; n*n - (n/2)*(n/2) < m || n*((n+1)/2) < j; n++);

			f.out(n + "\n");
			ans = new int[n][n];

			for(i = 1, x = 0; i < n && x < k; i+=2)
			{
				for(j = 0; j < n && x < k; j+=2)
				{
					ans[i][j] = a[x].n;

					a[x].f--;

					while(x < k && a[x].f == 0)
						x++;
				}
			}

			for(i = 0; i < n && x < k; i+=2)
			{
				for(j = 0; j < n && x < k; j+=2)
				{
					ans[i][j] = a[x].n;

					a[x].f--;

					while(x < k && a[x].f == 0)
						x++;
				}
			}

			for(i = 0; i < n && x < k; i+=2)
			{
				for(j = 1; j < n && x < k; j+=2)
				{
					ans[i][j] = a[x].n;

					a[x].f--;

					while(x < k && a[x].f == 0)
						x++;
				}
			}

			for(i = 0; i < n; i++)
			{
				for(j = 0; j < n; j++)
					f.out(ans[i][j] + " ");
				f.out("\n");
			}
		}

		f.flush();
	}

	static class Pair
	{
		int n, f;
	
		Pair(int x, int y)
		{
			n = x;
			f = y;
		}
	
		@Override
		public int hashCode()
		{
			return n;
		}
	
		@Override
		public boolean equals(Object obj)
		{
			Pair that = (Pair)obj;
	
			return n == that.n;
		}
	
		@Override
		public String toString()
		{
			return "[" + n + ", " + f + "]";
		}
	}

	public static class FastIO
	{
		BufferedReader br;
		BufferedWriter bw, be;
		StringTokenizer st;

		public FastIO()
		{
			br = new BufferedReader(new InputStreamReader(System.in));
			bw = new BufferedWriter(new OutputStreamWriter(System.out));
			be = new BufferedWriter(new OutputStreamWriter(System.err));
			st = new StringTokenizer("");
		}

		private void read() throws IOException
		{
			st = new StringTokenizer(br.readLine());
		}

		public String ns() throws IOException
		{
			while(!st.hasMoreTokens())
				read();
			return st.nextToken();
		}

		public int ni() throws IOException
		{
			return Integer.parseInt(ns());
		}

		public long nl() throws IOException
		{
			return Long.parseLong(ns());
		}

		public float nf() throws IOException
		{
			return Float.parseFloat(ns());
		}

		public double nd() throws IOException
		{
			return Double.parseDouble(ns());
		}

		public char nc() throws IOException
		{
			return ns().charAt(0);
		}

		public int[] nia(int n) throws IOException
		{
			int[] a = new int[n];
			for(int i = 0; i < n; i++)
				a[i] = ni();

			return a;
		}

		public long[] nla(int n) throws IOException
		{
			long[] a = new long[n];
			for(int i = 0; i < n; i++)
				a[i] = nl();

			return a;
		}

		public char[] nca() throws IOException
		{
			return ns().toCharArray();
		}

		public void out(String s) throws IOException
		{
			bw.write(s);
		}

		public void flush() throws IOException
		{
			bw.flush();
			be.flush();
		}

		public void err(String s) throws IOException
		{
			be.write(s);
		}
	}
}