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;
#define int long long
void read (int &x) {
    char ch = getchar(); x = 0; while (!isdigit(ch)) ch = getchar();
    while (isdigit(ch)) x = x * 10 + ch - 48, ch = getchar();
} const int N = 2e5 + 5, M = 2000, NN = N * 5;
int n, s, mx, a[N], res[M][M], sr, sb, sy, id[N];
pair<int, int> r[NN], b[NN], y[NN];
#define xx first
#define yy second
int get () {
    int l = 0, r = 1000, mid, res = 0;
    while (l <= r) {
        mid = l + r >> 1;
        if (s <= mid * mid - (mid / 2) * (mid / 2) && a[1] <= mid * ((mid + 1) / 2))
            res = mid, r = mid - 1;
        else l = mid + 1;
    }
    return res;
}
signed main() {
    int T; read (T);
    while (T--) {
        read (s), read (n); mx = 0;
        for (int i = 1; i <= n; ++i) {
            read (a[i]), id[i] = i;
            if (a[i] > a[mx]) mx = i;
        }
        id[1] = mx, id[mx] = 1; swap (a[1], a[mx]);
        int len = get (); sr = sb = sy = 0;
        for (int i = 2; i <= len; i += 2)
            for (int j = 1; j <= len; j += 2) r[++sr] = {i, j};
        for (int i = 1; i <= len; i += 2)
            for (int j = 1; j <= len; j += 2) b[++sb] = {i, j};
        for (int i = 1; i <= len; i += 2)
            for (int j = 2; j <= len; j += 2) y[++sy] = {i, j};
        for (int i = 1; i <= len; ++i)
            for (int j = 1; j <= len; ++j) res[i][j] = 0;
        for (int i = 1; i <= n; ++i) {
            for (int j = 1; j <= a[i]; ++j) {
                if (sr) res[r[sr].xx][r[sr].yy] = id[i], --sr;
                else if (sb) res[b[sb].xx][b[sb].yy] = id[i], --sb;
                else res[y[sy].xx][y[sy].yy] = id[i], --sy;
            }
        }
        printf ("%d\n", len);
        for (int i = 1; i <= len; ++i) {
            for (int j = 1; j <= len; ++j) printf ("%d ", res[i][j]); puts ("");
        }
    }
    return 0;
}