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 <bits/stdc++.h>
using std::vector;
const int L = 1005;
int T, n, m, k, a[L][L];
struct Node { int x, y; };
vector<Node> vec;
void move(int &x, int &y) {
	if (x == -1) return;
	if (x & 1) {
		if (y & 1) {
			if (x + 2 > n) {
				if (y + 2 > n) y = 1, x = 2;
				else y += 2, x = 1;
			} else x += 2;
		} else {
			if (x + 2 > n) {
				if (y + 2 > n) y = 1, x = 1;
				else y += 2, x = 1;
			} else x += 2;
		}
	} else {
		if (x + 2 > n) {
			if (y + 2 > n) x = -1;
			else y += 2, x = 2;
		} else x += 2;
	}
}
bool check() {
	int x = 1, y = 2;
	for (int i = 1; i <= n; i++)
	    for (int j = 1; j <= n; j++)
	        a[i][j] = 0;
	for (int i = 0; i < vec.size(); i++) {
		for (int j = 1; j <= vec[i].y; j++) {
			if (x == -1) return false;
			a[x][y] = vec[i].x;
			move(x, y);
		}
	}
	#define In(x, y) (x > 0 && x <= n && y > 0 && y <= n)
	for (int i = 1; i <= n; i++)
		for (int j = 1; j <= n; j++)
			if (a[i][j] && (In(i - 1, j - 1) && a[i][j] == a[i - 1][j - 1] || In(i - 1, j + 1) && a[i][j] == a[i - 1][j + 1] ||
				In(i + 1, j - 1) && a[i][j] == a[i + 1][j - 1] || In(i + 1, j + 1) && a[i][j] == a[i + 1][j + 1])) return false;
	return true;
}
int main() {
	scanf("%d", &T);
	while (T--) {
		scanf("%d%d", &m, &k);
		vec.clear();
		for (int i = 1; i <= k; i++) {
			int x; scanf("%d", &x);
			if (x) vec.push_back({i, x});
		}
		if (m == 1) { printf("1\n%d\n", vec[0].x); continue; }
		std::sort(vec.begin(), vec.end(), [](Node a, Node b) { return a.y > b.y; });
		n = std::max(2, (int)sqrt(m));
		for (;; n++)
			if (check()) break;
		printf("%d\n", n);
		for (int i = 1; i <= n; i++)
			for (int j = 1; j <= n; j++)
				printf("%d%c", a[i][j], " \n"[j == n]);	
	}
	return 0;
}