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:
using namespace std;

#include <iostream>
#include <algorithm>
#include <vector>

#define MAXN 100005

int M,K,ans[1005][1005];

void solve() {
	cin >> M >> K;
	int mx = 0;
	vector<pair<int,int>> cnt;
	for(int i = 1;i <= K;++i) {
		int c;
		cin >> c;
		mx = max(mx,c);
		cnt.push_back({c,i});
	}
	sort(cnt.begin(),cnt.end(),[&](pair<int,int> p,pair<int,int> p2) {return p.first > p2.first;});
	for(int i = 1;i <= M;++i) {
		if(mx > i * ((i + 1) / 2)) continue;
		if(M > i * i - (i / 2) * (i / 2)) continue;
		vector<pair<int,int>> blue,yellow,red;
		for(int j = 0;j < i;++j) {
			for(int k = 0;k < i;++k) {
				ans[j][k] = 0;
				if((j + k) % 2 == 1) {
					if(j % 2 == 0) {
						yellow.push_back({j,k});
					}else{
						red.push_back({j,k});
					}
				}else{
					if(j % 2 == 0) {
						blue.push_back({j,k});
					}
				}
			}
		}


		for(int j = 0;j < K;++j) {
			vector<pair<int,int>> &cur = (yellow.empty() ? red : yellow);
			while(cnt[j].first && !cur.empty()) {
				pair<int,int> pos = cur.back();
				ans[pos.first][pos.second] = cnt[j].second;
				cur.pop_back();
				// cout << "Hello" << pos.first << " " << pos.second << " " << cnt[j].second << endl;
				cnt[j].first--;
			}
			while(cnt[j].first--) {
				pair<int,int> pos = blue.back();
				ans[pos.first][pos.second] = cnt[j].second;
				blue.pop_back();
			}
		}
		cout << i << endl;
		for(int j = 0;j < i;++j) {
			for(int k = 0;k < i;++k) {
				cout << ans[j][k] << " ";
			}
			cout << endl;
		}
		break;
	}
	return;
}

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