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>
#include <random>
#include <chrono>
using namespace std;
//#pragma GCC optimize("Ofast")
//#pragma GCC optimize ("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<ll,ll> pll;
typedef pair<double,double> pdd;
//mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
const int MOD1=1e9+7;
const int MOD2=998244353;
const ll INF=LLONG_MAX;
const ld PI=3.14159265358979323846;
ll gcd(ll a,ll b){if(b==0) return a; return gcd(b,a%b);}
ll fpow(ll a,ll b,ll m)
{
    if(!b) return 1;
    ll ans=fpow(a*a%m,b/2,m);
    return (b%2?ans*a%m:ans);
}
ll inv(ll a,ll m) {return fpow(a,m-2,m);}
#define MottoHayaku ios::sync_with_stdio(false);cin.tie(0);
#define rep(i,n) for(ll i=0;i<n;i++)
#define rep1(i,n) for(ll i=1;i<=n;i++)
#define repk(i,m,n) for(int i=m;i<n;i++)
#define F first
#define S second
#define pb push_back
#define SZ(a) ((ll)a.size())
#define reset(a) memset(a,0,SZ(a))
#define cd(a,b) ((a+b-1)/b)
#define pow2(a) (1LL<<a)
#define LB(a,x) (lower_bound(a.begin(),a.end(),x))
#define LPOS(a,x) (lower_bound(a.begin(),a.end(),x)-a.begin())
#define UB(a,x) (upper_bound(a.begin(),a.end(),x))
#define UPOS(a,x) (upper_bound(a.begin(),a.end(),x)-a.begin())
#define uni(c) c.resize(distance(c.begin(),unique(c.begin(),c.end())))
#define unisort(c) sort(c.begin(),c.end()),uni(c)

signed main()
{
    MottoHayaku
    ll t;
    cin>>t;
    while(t--)
    {
        ll m,k,mx=0,id=-1;
        cin>>m>>k;
        vector<ll> a(k+1);
        set<ll> s;
        rep1(i,k)
        {
            cin>>a[i];
            if(mx<a[i]) mx=a[i],id=i;
            if(a[i]>0) s.insert(i);
        }
        ll n=1;
        while(m>((n+1)/2)*(3*n/2)||mx>(n+1)/2*n) n++;
        vector<vector<ll> > b(n,vector<ll>(n,0));
        ll x=1,y=0,cur=id;
        bool z=0;
        while(x<n&&!z)
        {
            b[x][y]=cur;
            a[cur]--;
            y+=2;
            if(y>=n) y=0,x+=2;
            if(a[cur]==0)
            {
                s.erase(cur);
                if(s.empty())
                {
                    z=1;
                    break;
                }
                cur=*s.begin();
            }
        }
        x=0,y=0;
        while(x<n&&!z)
        {
            b[x][y]=cur;
            a[cur]--;
            y+=2;
            if(y>=n) y=0,x+=2;
            if(a[cur]==0)
            {
                s.erase(cur);
                if(s.empty())
                {
                    z=1;
                    break;
                }
                cur=*s.begin();
            }
        }
        x=0,y=1;
        while(x<n&&!z)
        {
            b[x][y]=cur;
            a[cur]--;
            y+=2;
            if(y>=n) y=1,x+=2;
            if(a[cur]==0)
            {
                s.erase(cur);
                if(s.empty())
                {
                    z=1;
                    break;
                }
                cur=*s.begin();
            }
        }
        cout<<n<<"\n";
        rep(i,n)
        {
            rep(j,n) cout<<b[i][j]<<" ";
            cout<<"\n";
        }
    }
}