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:
//#pragma comment(linker, "/stack:200000000")
//#pragma GCC optimize("Ofast")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
//#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#define FINAL_OUT(x) {cout << (x) << '\n'; exit(0); }
inline int safe_mul(const int x, const int y) __attribute__ ((warn_unused_result));

int const maxn = 800;
int matr[maxn][maxn];

inline void ne(int& x, int& y, const int n) {
    y += 2;
    if (y >= n) {
        y &= 1;
        x += 2;
    }
    if (x >= n) {
        if (x%2 == 0 && y%2 == 1) {
            x = 1;
            y = 0;
        }
    }
}


inline bool ch(const int x, const int y, const int val, const int n) {
    return x < 0 || x >= n || y < 0 || y >= n || matr[x][y] != val;
}


inline bool good(const int x, const int y, const int val, const int n) {
    return ch(x-1, y-1, val, n) && ch(x-1, y+1, val, n) && ch(x+1, y-1, val, n) && ch(x+1, y+1, val, n);
}

bool check(const int n, const vector<int>& a) {
    for (int i = 0; i < n; ++i)
        fill(matr[i], matr[i] + n, 0);
    vector<pair<int,int>> mask;
    for (int i = 0; i < a.size(); ++i)
        if (a[i] > 0)
            mask.emplace_back(a[i], i + 1);
    sort(mask.rbegin(), mask.rend());
    int x = 0;
    int y = 1;
    int x2 = 0;
    int y2 = 0;
    bool ex = false;
    for (auto& [cnt, val] : mask) {
        while (cnt--) {
            if (x < n && y < n && good(x,y,val, n)) {
                matr[x][y] = val;
                ne(x,y,n);
            } else {
                if (ex || x2 >= n || y2 >= n)
                    return false;
                matr[x2][y2] = val;
                ne(x2,y2,n);
            }
        }
    }

    for (int i = 0; i + 1 < n; ++i)
        for (int j = 0; j + 1 < n; ++j) {
            int cnt = (matr[i][j] == 0) + (matr[i+1][j+1] == 0) + (matr[i+1][j] == 0) + (matr[i][j+1] == 0);
            if (cnt < 1 || (matr[i][j] == matr[i+1][j+1] && matr[i][j]) || (matr[i+1][j] == matr[i][j+1] && matr[i+1][j])) {
                return false;
            }
        }
    return true;
}

void solve() {
    int m,k;
    cin >> m >> k;
    vector<int> a(k);
    for (int& x : a)
        cin >> x;

    int l = 0;
    int r = min(maxn, m);
    while (r-l > 1) {
        int mid = (l+r) >> 1;
        if (check(mid, a))
            r = mid;
        else
            l = mid;
    }
    check(r, a);
    cout << r << '\n';
    for (int i = 0; i < r; ++i)
    for (int j = 0; j < r; ++j)
        cout << matr[i][j] << " \n"[j == r - 1];
}


int main()
{
//    freopen("in.txt", "r", stdin);
//    freopen("out.txt", "w", stdout);
    cout << fixed << setprecision(15);
    ios_base::sync_with_stdio(false);
    cin.tie(0), cout.tie(0);

    int t;
    cin >> t;
    while (t--) solve();
}