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;
#define MAXN 100005
#define lowbit(x) (x&-x)
#define reg register
#define mp make_pair
#define fir first
#define sec second
typedef long long LL;
typedef unsigned long long uLL;
const int INF=0x3f3f3f3f;
const LL mo=1e9+7;
const LL inv2=5e8+4;
const double Pi=acos(-1.0);
typedef pair<int,int> pii;
const double PI=acos(-1.0);
template<typename _T>
_T Fabs(_T x){return x<0?-x:x;}
template<typename _T>
void read(_T &x){
	_T f=1;x=0;char s=getchar();
	while(s>'9'||s<'0'){if(s=='-')f=-1;s=getchar();}
	while('0'<=s&&s<='9'){x=(x<<3)+(x<<1)+(s^48);s=getchar();}
	x*=f;
}
int k,m,t,b[1005][1005];
struct ming{int val,id;}a[MAXN];
bool check(int mid){
	if(1ll*mid*mid-1ll*(mid>>1LL)*(mid>>1LL)<m)return 0;
	return a[1].val<=1ll*mid*(mid+1LL>>1LL);
}
bool cmp(ming x,ming y){return x.val>y.val;}
signed main(){
	read(t);
	while(t--){
		read(m);read(k);for(int i=1;i<=k;i++)read(a[i].val),a[i].id=i;
		sort(a+1,a+k+1,cmp);int l=1,r=m,id=1;
		while(l<r){int mid=l+r>>1;if(check(mid))r=mid;else l=mid+1;}printf("%d\n",l);
		for(int i=1;i<=l;i+=2)for(int j=2;j<=l;j+=2){while(id<=k&&!a[id].val)id++;if(id<=k)b[i][j]=a[id].id,a[id].val--;}
		for(int i=1;i<=l;i+=2)for(int j=1;j<=l;j+=2){while(id<=k&&!a[id].val)id++;if(id<=k)b[i][j]=a[id].id,a[id].val--;}
		for(int i=2;i<=l;i+=2)for(int j=1;j<=l;j+=2){while(id<=k&&!a[id].val)id++;if(id<=k)b[i][j]=a[id].id,a[id].val--;}
		for(int i=1;i<=l;i++,puts(""))for(int j=1;j<=l;j++)printf("%d ",b[i][j]),b[i][j]=0;
	}
	return 0;
}
/*
11111
10101
11111
10101
11111

1111
1010
1111
1010
*/