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;

void solve()
{
    int m, k;
    cin >> m >> k;
    vector<pair<int, int>> a;
    vector<int> b;
    for (int i = 1; i <= k; i++)
    {
        int num;
        cin >> num;
        if (num)
            a.push_back({num, i});
    }
    sort(a.begin(), a.end(), greater<pair<int, int>>());
    for (auto [num, i] : a)
    {
        for (int j = 0; j < num; j++)
            b.push_back(i);
    }
    int MAX = sqrt(3 * m);
    vector<vector<int>> res(MAX + 2, vector<int>(MAX + 2));
    auto check = [&](int x) {
        int cnt = 0;
        int j = 0;
        auto insert = [&](int x, int y) {
            if (j < m)
                res[x][y] = b[j++];
        };
        auto P = [&](int x1, int y1, int x2, int y2) {
            if (res[x1][y1] == 0 || res[x2][y2] == 0)
                return true;
            return res[x1][y1] != res[x2][y2];
        };
        for (int i = 1; i <= x + 1; i++)
            for (int j = 1; j <= x + 1; j++)
                res[i][j] = 0;
        for (int i = 1; i <= x; i++)
        {
            for (int j = 1; j <= x; j++)
            {
                if ((i + j) & 1)
                {
                    if (j & 1)
                        insert(i, j);
                }
                else
                {
                    ;
                }
            }
        }
        for (int i = 1; i <= x; i++)
        {
            for (int j = 1; j <= x; j++)
            {
                if ((i + j) & 1)
                {
                    if (i & 1)
                        ;
                }
                else
                {
                    if ((i & 1) && (j & 1))
                        insert(i, j);
                }
            }
        }
        for (int i = 1; i <= x; i++)
        {
            for (int j = 1; j <= x; j++)
            {
                if ((i + j) & 1)
                {
                    if (i & 1)
                        insert(i, j);
                }
                else
                {
                    ;
                }
            }
        }

        if (j < m)
            return false;
        for (int i = 1; i <= x; i++)
        {
            for (int j = 1; j <= x; j++)
            {
                if (!P(i, j, i - 1, j - 1))
                    return false;
                if (!P(i, j, i + 1, j - 1))
                    return false;
            }
        }
        return true;
    };
    int l = 1, r = MAX;
    int ans = 0;
    while (l <= r)
    {
        int mid = (l + r) >> 1;
        //cout << l << " " << r << endl;
        if (check(mid))
        {
            r = mid - 1;
            ans = mid;
        }
        else
            l = mid + 1;
    }
    // //cout << check(2) << endl;
    // ans = 6;
    // cout << check(ans) << endl;
    check(ans);
    cout << ans << endl;
    for (int i = 1; i <= ans; i++)
    {
        for (int j = 1; j <= ans; j++)
        {
            cout << res[i][j] << " ";
        }
        cout << endl;
    }
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int T = 1;
    cin >> T;
    while (T--)
    {
        solve();
    }
}