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 m, k;
vector<int> q;
vector<int> ids;
vector<vector<int>> b;

int tryBuild(int n) {
    int n2 = n / 2, n2_ = (n + 1) / 2;
    int zeros = n2 * n2;
    int any = n2_ * n2_;
    int imp = n2 * n2_;
    if (m > 2 * imp + any) return 0;
    if (q[ids[0]] > any + imp) return 0;
    cerr << n << " :n\n";
    b.assign(n, vector<int>(n, 0));
    int i = 0;
    auto nxt = [&]() -> int {
        while (i < k && q[ids[i]] == 0) i++;
        if (i == k) return 0;
        q[ids[i]]--;
        return ids[i] + 1;
    };

    for (int i = 0; i < n; i += 2) for (int j = 1; j < n; j += 2) b[i][j] = nxt();
    for (int i = 0; i < n; i += 2) for (int j = 0; j < n; j += 2) b[i][j] = nxt();
    for (int i = 1; i < n; i += 2) for (int j = 0; j < n; j += 2) b[i][j] = nxt();

    return 1;
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);

    int t;
    cin >> t;
    while (t--) {
        cin >> m >> k;
        q.assign(k, 0);
        for (int i = 0; i < k; i++) cin >> q[i];
        
        ids.clear();
        for (int i = 0; i < k; i++) ids.push_back(i);
        sort(ids.begin(), ids.end(), [&](int i, int j) { return q[i] > q[j]; });

        int n = 1;
        while (!tryBuild(n)) n++;

        cout << n << "\n";
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) cout << b[i][j] << " ";
            cout << "\n";
        }
    }
}