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>
typedef int LL;
typedef double dl;
#define opt operator
#define pb push_back
#define pii std::pair<LL,LL>
const LL maxn=1e6+9,mod=998244353,inf=0x3f3f3f3f;
LL Read(){
	LL x(0),f(1); char c=getchar();
	while(c<'0' || c>'9'){
		if(c=='-') f=-1; c=getchar();
	}
	while(c>='0' && c<='9'){
		x=(x<<3ll)+(x<<1ll)+c-'0'; c=getchar();
	}return x*f;
}
void Chkmin(LL &x,LL y){
	if(y<x) x=y;
}
void Chkmax(LL &x,LL y){
	if(y>x) x=y;
}
LL add(LL x,LL y){
	return x+=y,x>=mod?x-mod:x;
}
LL dec(LL x,LL y){
	return x-=y,x<0?x+mod:x;
}
LL mul(LL x,LL y){
	return 1ll*x*y%mod;
}
LL Pow(LL base,LL b){
	LL ret(1); while(b){
		if(b&1) ret=mul(ret,base); base=mul(base,base); b>>=1;
	}return ret;
}
LL T,m,K;
LL ans[1009][1009],a[maxn];
bool cmp(pii A,pii B){
	return A>B;
}
void Change(pii A,LL c){
	ans[A.first][A.second]=c;
}
void Solve(){
	static pii p[maxn];
	m=Read(); K=Read();
	LL mx(0),sum(0);
	for(LL i=1;i<=K;++i){ 
		a[i]=Read(),Chkmax(mx,a[i]),sum+=a[i];
		p[i]=pii(a[i],i);
	}
	std::sort(p+1,p+1+K,cmp);
	LL n(1);
    for(;;++n){
		if(n*n-(n/2)*(n/2)<sum || (n+1)/2*n<mx) continue;
		break;
	}
	std::vector<pii> x,y,z;
	for(LL i=1;i<=n;++i){
		for(LL j=1;j<=n;++j){
			if((i+j)&1){
				if(i&1){
					x.pb(pii(i,j));
				}else{
					y.pb(pii(i,j));
				}
			}else{
				if(i&1){
					z.pb(pii(i,j));
				}
			}
		}
	}
	for(LL i=1;i<=n;++i){
		for(LL j=1;j<=n;++j) ans[i][j]=0;
	}
	for(LL i=1;i<=K;++i){
		LL c(p[i].second),num(p[i].first);
		std::vector<pii> &cur(x.empty()?y:x);
		while(num && cur.size()){
			Change(cur.back(),c);
			--num;
			cur.pop_back();
		}
		while(num--){
			assert(z.size());
			Change(z.back(),c);
			z.pop_back();
		}
	}
	printf("%d\n",n);
	for(LL i=1;i<=n;++i){
		for(LL j=1;j<=n;++j) printf("%d ",ans[i][j]);
		puts("");
	}//puts("");
}
int main(){
	T=Read();
	while(T--){
		Solve();
	}
	return 0;
}