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;

const int N = 1e5 + 10;

int main() {
	int t;
	cin >> t;
	while (t--) {
		int m, k;
		cin >> m >> k;
		pair <int, int> a[N];
		for (int i = 1; i <= k; ++i) {
			cin >> a[i].first;
			a[i].second = i;
		}
		sort(a + 1, a + k + 1, greater <pair<int, int>> ());
		int mx = a[1].first;
		for (int n = 1; n <= m; ++n) {
			// cout << n << endl;
			if (mx > 1ll* n * ((n + 1) / 2)) continue;
			if (m > 1ll * n * n - 1ll * (n / 2) * (n / 2)) continue;
			vector <pair<int, int>> x, y, z;
			for(int i = 1; i <= n; ++i) 
				for(int j = 1; j <= n; ++j) {
					if((i + j) % 2 == 0) {
						if(i % 2 == 1) z.push_back({i, j});
					} else {
						if(j % 2 == 0) x.push_back({i, j});
						else y.push_back({i, j});
					}
				}
			int ans[n + 1][n + 1];
			memset(ans, 0, sizeof(ans));
			cout << n << endl;
			for(int i = 1; i <= k; ++i) {
				vector<pair<int, int>> *cur = &(x.empty() ? y : x);
				while(a[i].first && !cur->empty()) {
					pair <int, int> now = cur->back();
					cur->pop_back();
					ans[now.first][now.second] = a[i].second;
					a[i].first --;
				}
				while(a[i].first) {
					pair <int, int> now = z.back();
					z.pop_back();
					ans[now.first][now.second] = a[i].second;
					--a[i].first;
				}
				
			}
			for(int i = 1; i <= n; ++i) {
				for(int j = 1; j <= n; ++j) {
					cout << ans[i][j] << " ";
				}
				cout << endl;
			}
			break;
		}
	}
}