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;
using pii = pair<int, int>;

void solve() {
	int m, k;
	cin >> m >> k;

	vector<pii> a;

	int ai;
	for (int i = 1; i <= k; i++) {
		cin >> ai;
		a.push_back({ai, i});
	}

	sort(a.begin(), a.end(), greater<pii>());

	int n = 1;
	for (; ; n++) {
		if (m > n * n - (n / 2) * (n / 2)) continue;
		if (a[0].first > n * ((n + 1) / 2)) continue;
		break;
	}
	
	vector<pii> pos[3];
	for (int i = 0; i < n; i++) {
		for (int j = 0; j < n; j++) {
			int idx = ((i & 1) << 1) + (j & 1);
			if (idx != 3) 
				pos[idx].push_back({i, j});
		}
	}

	vector<vector<int>> ans(n, vector<int>(n, 0));

	for (auto [cnt, val] : a) {
		vector<pii> &curr = pos[1].empty() ? pos[2] : pos[1];

		for (; !curr.empty() && cnt > 0; cnt--) {
			auto [x, y] = curr.back();
			curr.pop_back();
			ans[x][y] = val;
		}
		for (; cnt > 0; cnt--) {
			auto [x, y] = pos[0].back();
			pos[0].pop_back();
			ans[x][y] = val;
		}
	}

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

int main() {
	ios_base::sync_with_stdio(0);
	cin.tie(0);

	int t;
	cin >> t;

	while (t--) {
		solve();
	}

	return 0;
}