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 GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4.1,sse4.2,avx,avx2,popcnt,tune=native")
#include <immintrin.h>
#include <emmintrin.h>
#define ford(i,a,n) for(i=a;i<=n;i++)
#define forb(i,n,a) for(i=n;i>=a;i--)
#pragma comment(linker, "/STACK:1024000000,1024000000") 
#pragma GCC optimize(2)
#include<bits/stdc++.h> 
#define ll long long
#define I128 __int128
#define ld long double
#define PB push_back
using namespace std;
const int MAXN=4e5+666,mod=998244353,N=505;//
const ll INF=0x7ffffffffffffff;
const double PI=acos(-1);
typedef pair<int,int> pii;
template<class T>inline void MAX(T &x,T y){if(y>x)x=y;}
template<class T>inline void MIN(T &x,T y){if(y<x)x=y;}
template<class T>inline void rd(T &x){x=0;char o,f=1;while(o=getchar(),o<48)if(o==45)f=-f;do x=(x<<3)+(x<<1)+(o^48);while(o=getchar(),o>47);x*=f;}
template<class T>inline T ksm(T x,T y){T ans=1;while(y>0){if(y&1)ans=ans*x%mod;x=x*x%mod;y>>=1;}return ans;}
template<class T>inline T GCD(T x,T y){if(x==1||y==1)return 1;if(y>x)swap(x,y);while(x%y!=0){x=x%y;swap(x,y);}return y;}
int x[1005][1005];
int ans;
struct T{int x,id; }a[MAXN];
int cmp(T t1,T t2){ return t1.x>t2.x; }
vector<int> v;
int cal1(int p){ if(p%2) return p*(p/2+1); return p*(p/2); }
int cal2(int p){ if(p%2) return cal2(p-1)+p*2-1; return p*p/4*3; }
int main()
{
	int m,n,i,j,k,t,mx,p; rd(t);
	while(t--)
	{
		rd(m); rd(n); mx=0;
		for(i=1;i<=n;i++)
		{
			rd(a[i].x);
			if(a[i].x>mx){ mx=a[i].x;  p=i; }
			a[i].id=i;
		}
		if(m==1){ cout<<"1\n"<<a[p].id<<"\n"; continue; }
		int l=2,r=1000;
		while(l<r)
		{
			int mid=l+r>>1;
		//	cout<<l<<" "<<r<<" "<<mid<<" "<<cal1(mid)<<"\n";
			if(cal1(mid)>=mx) r=mid;
			else l=mid+1;
		}
		ans=l;// cout<<l<<"***\n";
		l=2; r=1000;
		while(l<r)
		{
			int mid=l+r>>1;
			if(cal2(mid)>=m) r=mid;
			else l=mid+1;
		}
		MAX(ans,l);//cout<<l<<"***\n";
		for(i=1;i<=ans;i++) for(j=1;j<=ans;j++) x[i][j]=0;
		cout<<ans<<"\n";
		sort(a+1,a+n+1,cmp);
		int k=1;
		for(i=1;i<=ans;i+=2)
		{
			if(k>n) break;
			for(j=2;j<=ans;j+=2)
			{
				while(k<=n&&a[k].x==0) k++;
				if(k>n) break;
				x[i][j]=a[k].id; a[k].x--;
			}
		}
		for(i=1;i<=ans;i+=2)
		{
			if(k>n) break;
			for(j=1;j<=ans;j+=2)
			{
				while(k<=n&&a[k].x==0) k++;
				if(k>n) break;
				x[i][j]=a[k].id; a[k].x--;
			}
		}
		for(i=2;i<=ans;i+=2)
		{
			if(k>n) break;
			for(j=1;j<=ans;j+=2)
			{
				while(k<=n&&a[k].x==0) k++;
				if(k>n) break;
				x[i][j]=a[k].id; a[k].x--;
			}
		}
		for(i=1;i<=ans;i++)
		{ for(j=1;j<=ans;j++) cout<<x[i][j]<<" "; cout<<"\n"; }
	}
}