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>
#define rep(i,a,b) for(int i=(a);i<=(b);++i)
#define per(i,a,b) for(int i=(a);i>=(b);--i)
#define ll long long
using namespace std;
inline ll read(){
    ll x=0,f=1;char ch=getchar();
    while (!isdigit(ch)){if (ch=='-') f=-1;ch=getchar();}
    while (isdigit(ch)){x=x*10+ch-48;ch=getchar();}
    return x*f;
}
const int N=1e5+5;
#define pii pair<int,int>
int m,k,mx;
inline void solve(){
    m=read(),k=read();
    pii a[k+5];
    rep(i,1,k){
        a[i].first=read();a[i].second=i;
    }
    sort(a+1,a+k+1,greater<pair<int,int>>());
    mx=a[1].first;
    rep(n,1,m){
        if(mx>1ll*n*((n+1)/2))continue;
        if(m>1ll*n*n-1ll*(n/2)*(n/2))continue;
        vector<pii> x,y,z;
        rep(i,0,n-1){
            rep(j,0,n-1){
                if((i+j)&1){
                    if(i&1)y.push_back({i,j});
                    else x.push_back({i,j});
                }else if(i%2==0)z.push_back({i,j});
            }
        }
        int ans[n][n];
        rep(i,0,n-1)rep(j,0,n-1)ans[i][j]=0;
        rep(i,1,k){
            vector<pii> &cur = (x.empty() ? y : x);
            while(a[i].first&&!cur.empty()){
                pii pos=cur.back();ans[pos.first][pos.second]=a[i].second;
                cur.pop_back();--a[i].first;
            }
            while(a[i].first){
                pii pos=z.back();ans[pos.first][pos.second]=a[i].second;
                z.pop_back();--a[i].first;
            }
        }
        printf("%d\n",n);
        rep(i,0,n-1){
            rep(j,0,n-1)printf("%d ",ans[i][j]);puts("");
        }
        break;
    }
}
int main(){
    int T=read();
    while(T--)solve();
    return 0;
}