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>
#define X first
#define Y second

using namespace std;

const long long inf = 1000000000000000;
const long long MAXN = 100000+9;
const long long MAX_ANS = 500+9;

long long n, m, k, t, temp, ans, res, ok, sum, maxi, max_pos;
vector <long long> v;
long long x[MAXN], matrix[MAX_ANS][MAX_ANS];

long long f1(int n){
    if (n%2 == 0)
        return (n/2)*(n/2);
    if (n%2 == 1)
        return (n/2)*(n+1)/2;
}

long long f2(int n){
    if (n%2 == 0)
        return (n/2)*(n/2);
    if (n%2 == 1)
        return (n+1)*(n+1)/4;
}

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL); cout.tie(NULL);

    cin >> t;
    for (int uu = 1; uu <= t; uu++){
        cin >> sum >> k;
        v.clear();
        maxi = -1;
        for (int i = 1; i <= k; i++){
            cin >> x[i];
            if (x[i] > maxi){
                maxi = x[i];
                max_pos = i;
            }
        }

        for (int i = 1; i <= 500; i++)
            if (2*f1(i) + f2(i) >= sum && f1(i) + f2(i) >= maxi){
                ans = i;
                break;
            }

        cout << ans << '\n';
        for (int i = 1; i <= x[max_pos]; i++)
            v.push_back(max_pos);
        x[max_pos] = 0;
        for (int i = 1; i <= k; i++)
            for (int j = 1; j <= x[i]; j++)
                v.push_back(i);

        temp = 0;
        for (int i = 2; i <= ans; i += 2)
            for (int j = 1; j <= ans; j += 2)
                matrix[i][j] = (temp < v.size()) ? v[temp++] : 0;
        for (int i = 1; i <= ans; i += 2)
            for (int j = 1; j <= ans; j += 2)
                matrix[i][j] = (temp < v.size()) ? v[temp++] : 0;
        for (int i = 1; i <= ans; i += 2)
            for (int j = 2; j <= ans; j+= 2)
                matrix[i][j] = (temp < v.size()) ? v[temp++] : 0;

        for (int i = 1; i <= ans; i++){
            for (int j = 1; j <= ans; j++)
                cout << matrix[i][j] << ' ';
            cout << '\n';
        }
    }
}