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 <cstring>
using namespace std;

int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(nullptr);

	int max_m[450], max_ModeCount[450];
	for (int i = 1; i < 450; i++)
	{
		max_m[i] = i * i - (i / 2) * (i / 2);
		max_ModeCount[i] = i * ((i + 1) / 2);
 	}

	int t;
	cin >> t;
	int m, k, a[100001], Ans[600][600];
	int aa[100001], iO, oO;
	pair<int, int> Order[300000];
	while (t--)
	{
		cin >> m >> k;
		int ModeValue, ModeCount = 0;
		for (int i = 1; i <= k; i++)
		{
			cin >> a[i];
			if (ModeCount < a[i])
				ModeCount = a[i], ModeValue = i;
		}

		if (m == 1)
		{
			cout << "1\n" << ModeValue << "\n";
			continue;
		}

		int n1 = 2, n2 = 2;
		while (m > max_m[n1]) n1++;
		while (ModeCount > max_ModeCount[n2]) n2++;

		int n = max(n1, n2) - 1;
		bool Re = true;
		while (Re)
		{
			n++;
			Re = false;
			iO = 0, oO = 0;
			for (int i = 0; i < n; i += 2)
				for (int j = 1; j < n; j += 2)
				{
					Order[iO++] = make_pair(i, j);
				}
			for (int i = 0; i < n; i += 2)
				for (int j = 0; j < n; j += 2)
				{
					Order[iO++] = make_pair(i, j);
				}
			for (int i = 1; i < n; i += 2)
				for (int j = 0; j < n; j += 2)
				{
					Order[iO++] = make_pair(i, j);
				}
			
			for (int i = 0; i < n; i++)
				fill(Ans[i], Ans[i] + n + 1, 0);
			memcpy(aa, a, sizeof(int) * (k + 1));

			while (aa[ModeValue] > 0)
			{
				Ans[Order[oO].first][Order[oO].second] = ModeValue;
				oO++, aa[ModeValue]--;
			}
			for (int i = 1; i <= k; i++)
				while (aa[i] > 0)
				{
					Ans[Order[oO].first][Order[oO].second] = i;
					oO++, aa[i]--;
				}

			for (int i = 0; i < n - 1; i++)
				for (int j = 1; j < n; j++)
					if (Ans[i][j] != 0 && Ans[i][j] == Ans[i + 1][j - 1])
						Re = true;
			for (int i = 0; i < n - 1; i++)
				for (int j = 0; j < n - 1; j++)
					if (Ans[i][j] != 0 && Ans[i][j] == Ans[i + 1][j + 1])
						Re = true;
		}

		cout << n << "\n";
		for (int i = 0; i < n; i++)
		{
			for (int j = 0; j < n; j++)
				cout << Ans[i][j] << " ";
			cout << "\n";
		}
	}

	return 0;
}