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;

int n,m,k,mx,a[100005],b[505][505],c[100005];

void mian(){
    cin>>m>>k;
    mx=0;
    vector<pair<int,int>> v;
    for(int i=1;i<=k;i++){
        cin>>a[i];
        mx=max(mx,a[i]);
        v.emplace_back(a[i],i);
    }
    n=1;
    while(m>n*n-(n/2)*(n/2)||mx>(n+1)/2*n)n++;
    for(int i=1;i<=n;i++)memset(b[i]+1,0,n<<2);
    sort(v.begin(),v.end());
    reverse(v.begin(),v.end());
    m=0;
    for(pair<int,int> &p:v){
        while(p.first--)c[++m]=p.second;
    }
    int cm=0;
    for(int i=1;i<=n;i++)for(int j=1;j<=n;j++){
        if(i&1&&j&1^1&&cm<m)b[i][j]=c[++cm];
    }
    for(int i=1;i<=n;i++)for(int j=1;j<=n;j++){
        if(i&1&&j&1&&cm<m)b[i][j]=c[++cm];
    }
    for(int i=1;i<=n;i++)for(int j=1;j<=n;j++){
        if(i&1^1&&j&1&&cm<m)b[i][j]=c[++cm];
    }
    cout<<n<<'\n';
    for(int i=1;i<=n;i++){
        for(int j=1;j<=n;j++){
            cout<<b[i][j]<<' ';
        }
        cout<<'\n';
    }
}

int main(){

    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);

    int T;
    cin>>T;
    while(T--)mian();

    return 0;
}