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>

void solve() {
	int m, n;
	std::cin >> m >> n;
	std::vector<int> a(n);
	for (int i = 0; i < n; ++i) {
		std::cin >> a[i];
	}
	int mx = *std::max_element(a.begin(), a.end());

	auto check = [&](int x) {
		long long c1 = 1ll * ((x + 1) / 2) * (x / 2);
		long long c2 = 1ll * ((x + 1) / 2) * ((x + 1) / 2);
		return mx <= c1 + c2 && m <= c1 * 2 + c2;
	};

	int l = 1, r = m, x = 0;
	while (l <= r) {
		int mid = (l + r) >> 1;
		if (check(mid)) {
			r = mid - 1;
			x = mid;
		} else {
			l = mid + 1;
		}
	}

	std::vector<int> val;
	for (int i = 0; i < n; ++i) {
		for (int j = 0; j < a[i]; ++j) {
			val.push_back(i);
		}
	}
	std::sort(val.begin(), val.end(), [&](int x, int y) {
		return a[x] < a[y] || (a[x] == a[y] && x < y);
	});

	std::vector<std::vector<int>> ans(x, std::vector<int>(x, -1));
	for (int i = 0; i < x; ++i) {
		for (int j = 0; j < x; ++j) {
			if (!(i & 1) && (j & 1) && !val.empty()) {
				ans[i][j] = val.back();
				val.pop_back();
			}
		}
	}
	for (int i = 0; i < x; ++i) {
		for (int j = 0; j < x; ++j) {
			if (!(i & 1) && !(j & 1) && !val.empty()) {
				ans[i][j] = val.back();
				val.pop_back();
			}
		}
	}
	for (int i = 0; i < x; ++i) {
		for (int j = 0; j < x; ++j) {
			if ((i & 1) && !(j & 1) && !val.empty()) {
				ans[i][j] = val.back();
				val.pop_back();
			}
		}
	}
	std::cout << x << "\n";
	for (int i = 0; i < x; ++i) {
		for (int j = 0; j < x; ++j) {
			std::cout << ans[i][j] + 1 << " ";
		}
		std::cout << "\n";
	}
}

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

	int T;
	std::cin >> T;
	while (T--) {
		solve();
	}
}