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:
/**
 *  created: 07/05/2021, 19:15:34
**/

#include <bits/stdc++.h>

using namespace std;

const int max_n = 100111, inf = 1000111222;
const int max_r = 700;

int t, m, k, ans[max_r][max_r];
vector<pair<int, int>> v;
vector<int> all;

void clr() {
    v.clear();
    all.clear();
}

bool good(int n) {
    for (int i = 0; i + 1 < n; ++i) {
        for (int j = 0; j + 1 < n; ++j) {
            if (ans[i][j] && ans[i + 1][j] && ans[i][j + 1] && ans[i + 1][j + 1]) {
                return false;
            }
            if (ans[i][j] && ans[i][j] == ans[i + 1][j + 1]) {
                return false;
            }
            if (ans[i][j + 1] && ans[i][j + 1] == ans[i + 1][j]) {
                return false;
            }
        }
    }
    return true;
}

bool check(int n) {
    if (n == 1) {
        if (all.size() == 1) {
            ans[0][0] = all[0];
            return true;
        }
        return false;
    }
    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < n; ++j) {
            ans[i][j] = 0;
        }
    }
    int tp = 1;
    int row = 0, col = 1;
    for (int x : all) {
        if (row == -1) {
            return false;
        }
        ans[row][col] = x;
        col += 2;
        if (col >= n) {
            row += 2;
            col %= 2;
            if (row >= n) {
                ++tp;
                col = 0;
                if (tp == 4) {
                    row = -1;
                } else if (tp == 2) {
                    row = 0;
                } else {
                    row = 1;
                }
            }
        }
    }
    return good(n);
}

int main() {
    //freopen("input.txt", "r", stdin);
    //freopen("output.txt", "w", stdout);
    scanf("%d", &t);
    while (t--) {
        clr();
        scanf("%d%d", &m, &k);
        for (int i = 1; i <= k; ++i) {
            int c;
            scanf("%d", &c);
            v.push_back({c, i});
        }
        sort(v.begin(), v.end());
        reverse(v.begin(), v.end());
        for (auto p : v) {
            for (int i = 0; i < p.first; ++i) {
                all.push_back(p.second);
            }
        }
        int max_ans = 1;
        while (m > max_ans * max_ans) {
            ++max_ans;
        }
        max_ans *= 2;
        //cout << "#" << max_ans << endl;
        /*for (int x = 1; x <= 10; ++x) {
            cout << x << ": " << check(x) << endl;
        }
        cout << check(2) << endl;
        return 0;*/
        int l = 0, r = max_ans + 5;
        while (r - l > 1) {
            int mid = (l + r) / 2;
            if (check(mid)) {
                r = mid;
            } else {
                l = mid;
            }
        }
        check(r);
        printf("%d\n", r);
        for (int i = 0; i < r; ++i) {
            for (int j = 0; j < r; ++j) {
                printf("%d ", ans[i][j]);
            }
            puts("");
        }
    }
    return 0;
}