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;
typedef pair<int, int> pii;

int M, K;
int ans[505][505];
pii A[101010];
vector<pii> v;

int main() {
	int tc; scanf("%d", &tc);
	while(tc--) {
		scanf("%d%d", &M, &K);
		for(int i = 1; i <= K; i++) {
			scanf("%d", &A[i].first);
			A[i].second = i;
		}
		sort(A + 1, A + K + 1);
		reverse(A + 1, A + K + 1);
		int l = 1, r = 500;
		while(l <= r) {
			int m = l + r >> 1;
			int t = m * m - (m / 2) * (m / 2);
			if(t < M) { l = m + 1; continue; }
			if(m * ((m + 1) / 2) < A[1].first) { l = m + 1; continue; }
			r = m - 1;
		}

		int N = l;
		int x = 1, y = 2;
		v.clear();
		while(x <= N && y <= N) {
			v.emplace_back(x, y);
			y += 2;
			if(y > N) { x += 2; y = 2; }
		}
		x = 1; y = 1;
		while(x <= N) {
			v.emplace_back(x, y);
			y += 2;
			if(y > N) { x += 2; y = 1; }
		}
		x = 2; y = 1;
		while(x <= N) {
			v.emplace_back(x, y);
			y += 2;
			if(y > N) { x += 2; y = 1; }
		}

		int p = 0;
		for(int i = 1; i <= N; i++) for(int j = 1; j <= N; j++) ans[i][j] = 0;
		for(int i = 1; i <= K; i++) {
			for(int j = 0; j < A[i].first; j++) {
				ans[v[p].first][v[p].second] = A[i].second;
				p++;
			}
		}

		printf("%d\n", N);
		for(int i = 1; i <= N; i++) {
			for(int j = 1; j <= N; j++) printf("%d ", ans[i][j]); puts("");
		}
	}
	return 0;
}