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 = 100000 + 5;
const int M = 1000;

int m;
int k;
int c[N];
int a[M][M];
vector<int> v;

void clear(int len){
	for(int i = 1; i <= len; i++){
		for(int j = 1; j <= len; j++){
			a[i][j] = 0;
		}
	}
}

bool check(int len){
	for(int i = 1; i + 1 <= len; i++){
		for(int j = 1; j + 1 <= len; j++){
			if(a[i][j] and a[i + 1][j + 1] and a[i][j] == a[i + 1][j + 1]) return false;
			if(a[i + 1][j] and a[i][j + 1] and a[i + 1][j] == a[i][j + 1]) return false;
		}
	}
	return true;
}

void print(int len){
	printf("%d\n", len);
	for(int i = 1; i <= len; i++){
		for(int j = 1; j <= len; j++){
			printf("%d%c", a[i][j], " \n"[j == len]);
		}
	}
}

void assign(int len){
	int pos = 0;
	for(int i = 1; i <= len and pos < v.size(); i += 2){
		for(int j = 2; j <= len and pos < v.size(); j += 2){
			a[i][j] = v[pos];
			pos += 1;
		}
	}
	for(int i = 1; i <= len and pos < v.size(); i += 2){
		for(int j = 1; j <= len and pos < v.size(); j += 2){
			a[i][j] = v[pos];
			pos += 1;
		}
	}

	for(int i = 2; i <= len and pos < v.size(); i += 2){
		for(int j = 1; j <= len and pos < v.size(); j += 2){
			a[i][j] = v[pos];
			pos += 1;
		}
	}
}

void solve(){
	int maximo = *max_element(c + 1, c +  1 + k);
	int lo = 1, hi = 200000;
	while(lo < hi){
		int mi = lo + (hi - lo) / 2;
		if(1ll * (mi - mi / 2) * mi < maximo or 1ll * mi * mi - 1ll * (mi / 2) * (mi / 2) < m){
			lo = mi + 1;
		}
		else{
			hi = mi;
		}
	}
	assign(lo);
	print(lo);
	clear(lo);
}

int main(){
	int t;
	scanf("%d", &t);
	while(t--){
		scanf("%d %d", &m, &k);
		for(int i = 1; i <= k; i++){
			scanf("%d", &c[i]);
		}
		vector<int> p(k);
		iota(p.begin(), p.end(), 1);
		sort(p.begin(), p.end(), [&] (int i, int j){
			return c[i] > c[j];
		});
		v.clear();
		for(int i : p){
			for(int j = 0; j < c[i]; j++) v.emplace_back(i);
		}
		solve();
	}
	return 0;
}