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 namespace std;

int a[100001];
pair<int, int> as[100001];
int grid[3001][3001];

int main()
{
	int T;
	cin >> T;
	for (int t = 1; t <= T; t++) {
		int m, k;
		cin >> m >> k;

		int most = 1;
		for (int i = 1; i <= k; i++) {
			cin >> a[i];
			if (a[i] > a[most]) most = i;
			as[i] = {a[i], i};
		}
		sort(as + 1, as + k + 1);

		int ll = 1, rr = min(3000, m);
		int n = -1;
		while (ll <= rr) {
			int mid = (ll + rr) / 2;
			if (mid * mid - (mid / 2) * (mid / 2) >= m && mid * ((mid + 1) / 2) >= a[most]) {
				n = mid;
				rr = mid - 1;
			} else {
				ll = mid + 1;
			}
		}

		if (n == 1) {
			cout << n << '\n';
			cout << as[k].second << '\n';
			continue;
		}

		int r = 1, c = 2;
		int r2 = 2, c2 = 1;
		int r3 = 1, c3 = 1;
		for (int i = k; i >= 1; i--) {
			if (r <= n) {
				for (int j = 1; j <= as[i].first; j++) {
					if (r > n) {
						grid[r3][c3] = as[i].second;
						c3 += 2;
						if (c3 > n) {
							c3 = 1;
							r3 += 2;
						}
					} else {
						grid[r][c] = as[i].second;
						c += 2;
						if (c > n) {
							c = 2;
							r += 2;
						}
					}
				}
			} else {
				for (int j = 1; j <= as[i].first; j++) {
					if (r2 > n) {
						grid[r3][c3] = as[i].second;
						c3 += 2;
						if (c3 > n) {
							c3 = 1;
							r3 += 2;
						}
					} else {
						grid[r2][c2] = as[i].second;
						c2 += 2;
						if (c2 > n) {
							c2 = 1;
							r2 += 2;
						}
					}
				}
			}
		}

		cout << n << '\n';
		for (int i = 1; i <= n; i++) {
			for (int j = 1; j <= n; j++) {
				cout << grid[i][j] << ' ';
				grid[i][j] = 0;
			}
			cout << '\n';
		}
	}
}