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 <cstdio>
#include <vector>
#include <algorithm>
using namespace std;
#define maxn 100005
vector < pair < int, int > > G, R, B, Y;
int T, m, k, cnt, maxx;
int mp[1005][1005];

int find() {
	int l = 1, r = m, ans;
	while( l <= r ) {
		int mid = ( l + r ) >> 1;
		if( cnt <= 2 * ( ( mid + 1 ) / 2 ) * mid - ( ( mid + 1 ) / 2 ) * ( ( mid + 1 ) / 2 ) && maxx <= mid * ( ( mid + 1 ) / 2 ) )
			ans = mid, r = mid - 1;
		else
			l = mid + 1;
	}
	return ans;
}

int main() {
	scanf( "%d", &T );
	while( T -- ) {
		scanf( "%d %d", &m, &k );
		cnt = maxx = 0;
		G.clear(), R.clear(), B.clear(), Y.clear();
		for( int i = 1, x;i <= k;i ++ ) {
			scanf( "%d", &x );
			G.push_back( make_pair( x, i ) );
			cnt += x, maxx = max( maxx, x );
		}
		sort( G.begin(), G.end() );
		int n = find();
		printf( "%d\n", n );
		for( int i = 1;i <= n;i ++ )
			for( int j = 1;j <= n;j ++ )
				mp[i][j] = 0;
		for( int i = 1;i <= n;i += 2 )
			for( int j = 1;j <= n;j += 2 )
				B.push_back( make_pair( i, j ) );
		for( int i = 2;i <= n;i += 2 )
			for( int j = 1;j <= n;j += 2 )
				R.push_back( make_pair( i, j ) );
		for( int i = 1;i <= n;i += 2 )
			for( int j = 2;j <= n;j += 2 )
				Y.push_back( make_pair( i, j ) );
		for( int i = G.size() - 1;~ i;i -- )
			while( G[i].first ) {
				G[i].first --;
				if( ! R.empty() ) mp[R.back().first][R.back().second] = G[i].second, R.pop_back();
				else if( ! B.empty() ) mp[B.back().first][B.back().second] = G[i].second, B.pop_back();
				else mp[Y.back().first][Y.back().second] = G[i].second, Y.pop_back();
			}
		for( int i = 1;i <= n;i ++ ) {
			for( int j = 1;j <= n;j ++ )
				printf( "%d ", mp[i][j] );
			printf( "\n" );
		}
	}
	return 0;
}