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;
#define INF 2047483647
#define INFL 9223372036854775807
#define ll long long
#define pii pair<int,int>
#define F first
#define S second
#define mp make_pair
#define pb push_back
#define ull unsigned long long
#define MM 1000000007
#define FASTIO ios_base::sync_with_stdio(false);cin.tie(NULL); cout.tie(NULL);
#define take(x) scanf("%d",&x)
#define DE(x) printf("\ndebug %d\n",x);
#define vout(x) for(int i=0;i<x.size();i++) printf("%d ",x[i]);
#define pie acos(-1)
#define MOD 998244353

vector<int> seq,pos;
void pre(){
    seq.pb(0);
    pos.pb(0);
    for(int i=1;;i++){
        int val = i * ( (i+1)/2 );
        seq.pb(val);
        int plus = (i/2)* ((i+1)/2);
        pos.pb(val+plus);

        if( val>2*10e5 ) break;
    }
}
void solve(){
    int k,n;
    cin>>k>>n;
    pii para[n];
    for(int i=0;i<n;i++){
        cin>>para[i].F;
        para[i].S = i+1;
    }
    sort(para,para+n);
    reverse(para,para+n);
    int pos1 = lower_bound(seq.begin(),seq.end(),para[0].F) - seq.begin();
    int pos2 = lower_bound(pos.begin(),pos.end(),k) - pos.begin();
    int sz = max(pos1,pos2);
    int res[sz][sz];
    for(int i=0;i<sz;i++){
        for(int j=0;j<sz;j++)
            res[i][j] = 0;

    }
    int position = 0;
    bool flag = true;
    for(int i=0;i<sz;i+=2){
        for(int j=0;j<sz;j++){
            if( position == n or para[position].F == 0 ) {
                break;
            }
            res[i][j] = para[position].S;
            //cout<<para[position].S<<" ";
            para[position].F--;
            if( para[position].F == 0 ) position++;

        }
        if(!flag) break;
    }
    for(int i=1;i<sz;i+=2){
        for(int j=0;j<sz;j+=2){
            if( position == n or para[position].F == 0 ) {
                break;
            }
            res[i][j] = para[position].S;
            para[position].F--;
            if( para[position].F == 0 ) position++;

        }
        if(!flag) break;
    }
    int posx = 00,posy=0;
    for(int i=1;i<sz;i++){
        for(int j=1;j<sz;j++){
            if( res[i][j] == res[i-1][j-1] and res[i][j]!=0){
                swap( res[i][j],res[posx][posy] );
                posy+=2;
                if( posy >= sz ) {
                    posy = 0;
                    posx+=2;
                }
                if( posx >= sz ) { posx = 0; posy = 1; }
            }
        }
    }
    cout<<sz<<endl;
    for(int i=0;i<sz;i++){
        for(int j=0;j<sz;j++)
            cout<<res[i][j]<<" ";
        cout<<endl;
    }
}

int main(){
    pre();



    int tc;
    cin>>tc;
    while(tc--){
        solve();
    }
}