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;

template<typename elemType>
inline void Read(elemType& T) {
    elemType X = 0, w = 0; char ch = 0;
    while (!isdigit(ch)) { w |= ch == '-'; ch = getchar(); }
    while (isdigit(ch)) X = (X << 3) + (X << 1) + (ch ^ 48), ch = getchar();
    T = (w ? -X : X);
}

int G[1005][1005];
vector<pair<int, int> > vec, temp;
int T, m, k;

bool cmp(pair<int, int>& A, pair<int, int>& B) {
    if (A.first == B.first) return A.second < B.second;
    return A.first > B.first;
}

void construct(int n) {
    int p = 0;
    for (int i = 2;i <= n;i += 2) {
        for (int j = 1;j <= n;j += 2) {
            if (p >= vec.size()) break;
            if (!vec[p].first) ++p;
            if (p >= vec.size()) break;
            G[i][j] = vec[p].second; --vec[p].first;
        }
    }
    for (int i = 1;i <= n;i += 2) {
        for (int j = 1;j <= n;j += 2) {
            if (p >= vec.size()) break;
            if (!vec[p].first) ++p;
            if (p >= vec.size()) break;
            G[i][j] = vec[p].second;--vec[p].first;
        }
    }
    for (int i = 1;i <= n;i += 2) {
        for (int j = 2;j <= n;j += 2) {
            if (p >= vec.size()) break;
            if (!vec[p].first) ++p;
            if (p >= vec.size()) break;
            G[i][j] = vec[p].second;--vec[p].first;
        }
    }
    for (int i = 1;i <= n;++i) {
        for (int j = 1;j <= n;++j) {
            printf("%d", G[i][j]);
            if (j < n) printf(" ");
            G[i][j] = 0;
        }
        printf("\n");
    }
}

int main() {
    Read(T);
    while (T--) {
        Read(m); Read(k);
        vec.clear();
        for (int i = 1; i <= k; ++i) {
            int x; Read(x);
            if (x) vec.push_back(make_pair(x, i));
        }
        sort(vec.begin(), vec.end(), cmp);
        int n = 1;
        for (n = 1;;++n)
            if (n * n - (n / 2) * (n / 2) >= m && n * ((n + 1) / 2) >= vec[0].first) break;
        printf("%d\n", n);
        construct(n);
    }
    return 0;
}