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

    int q;
    cin >> q;

    while (q--) {
        int m, k; cin >> m >> k;

        pair<int, int> a[k];
        for (int i = 0; i < k; ++i) {
            cin >> a[i].first, a[i].second = i + 1;
        } sort(a, a + k, greater<pair<int, int>>());

        int mx = a[0].first;
        for (int n = 1; n <= m; ++n) {
            // mx <= n * ceil(n / 2)
            if (mx > n * (long long)((n + 1) / 2)) continue;
            // m <= n ^ 2 - floor(n / 2) ^ 2
            if (m > n * (long long)n - (n / 2) * (long long)(n / 2)) continue;

            // answer = n
            vector<pair<int, int>> x, y, z;
            for (int i = 0; i < n; ++i) {
                for (int j = 0; j < n; ++j) {
                    if ((i + j) % 2 == 1) {
                        if (i % 2 == 0) x.push_back({i, j});
                        else y.push_back({i, j});
                    } else {
                        if (i % 2 == 0) z.push_back({i, j});
                    }
                }
            }

            int ans[n][n];
            for (int i = 0; i < n; ++i) {
                for (int j = 0; j < n; ++j) {
                    ans[i][j] = 0;
                }
            }

            for (int i = 0; i < k; ++i) {
                vector<pair<int, int>> &cur = (x.empty() ? y : x);
                while (a[i].first && !cur.empty()) {
                    pair<int, int> pos = cur.back();
                    ans[pos.first][pos.second] = a[i].second;
                    cur.pop_back(); --a[i].first;
                }
                while(a[i].first--) {
                    assert((int)z.size() > 0);
                    pair<int, int> pos = z.back();
                    ans[pos.first][pos.second] = a[i].second;
                    z.pop_back();
                }
            }

            // print answer
            cout << n << endl;
            for (int i = 0; i < n; ++i) {
                for (int j = 0; j < n; ++j) {
                    cout << ans[i][j] << ' ';
                } cout << endl;
            }

            break;
        }
    }
}