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 main() {
	cin.tie(nullptr)->sync_with_stdio(false);
	int tt;
	cin >> tt;
	while (tt--) {
		int m, k;
		cin >> m >> k;
		vector<int> a(k);
		for (int i = 0; i < k; i++) {
			cin >> a[i];
		}
		vector<int> p(k);
		iota(p.begin(), p.end(), 0);
		sort(p.begin(), p.end(), [&](const int &x, const int &y) {
			return a[x] > a[y];
		});
		int n = 0;
		auto check = [&](int n) {
			if (n * n - (n / 2) * (n / 2) < m) {
				return false;
			} else if (n * ((n + 1) / 2) < a[p[0]]) {
				return false;
			} else {
				return true;
			}
		};
		while (!check(++n));
		vector<vector<int>> ans(n, vector<int>(n, -1));
		vector<tuple<int, int>> position;
		for (int i = 0; i < n; i += 2) {
			for (int j = 1; j < n; j += 2) {
				position.emplace_back(i, j);
			}
		}
		for (int i = 0; i < n; i += 2) {
			for (int j = 0; j < n; j += 2) {
				position.emplace_back(i, j);
			}
		}
		for (int i = 1; i < n; i += 2) {
			for (int j = 0; j < n; j += 2) {
				position.emplace_back(i, j);
			}
		}
		int pos = 0;
		for (auto &x : p) {
			while (a[x]--) {
				int x0, y0;
				tie(x0, y0) = position[pos++];
				ans[x0][y0] = x;
			}
		}
		cout << n << "\n";
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < n; j++) {
				cout << ans[i][j] + 1 << " \n"[j + 1 == n];
			}
		}
	}
}