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;
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,avx,avx2,fma,tune=native")

#define ll long long
#define int ll
#define ull unsigned ll
#define ld long double
#define rep(a) rep1(i,a)
#define rep1(i,a) rep2(i,0,a)
#define rep2(i,b,a) for(int i=(b); i<((int)(a)); i++)
#define rep3(i,b,a) for(int i=(b); i>=((int)(a)); i--)
#define all(a) a.begin(),a.end()
#define pii pair<int,int>
#define pb push_back
//#define inf 1010000000
#define inf 4000000000000000000
#define eps 1e-9
#define sz(a) ((int)a.size())
#define pow2(x) (1ll<<(x))
#define ceiling(a,b) (((a)+(b)-1)/(b))
#define print0(a) cout << (a) << ' '
#define ykh mt19937 rng(chrono::steady_clock::now().time_since_epoch().count())
#ifdef i_am_noob
#define bug(...) cerr << "#" << __LINE__ << ' ' << #__VA_ARGS__ << "- ", _do(__VA_ARGS__)
template<typename T> void _do(vector<T> x){for(auto i: x) cerr << i << ' ';cerr << "\n";}
template<typename T> void _do(set<T> x){for(auto i: x) cerr << i << ' ';cerr << "\n";}
template<typename T> void _do(unordered_set<T> x){for(auto i: x) cerr << i << ' ';cerr << "\n";}
template<typename T> void _do(T && x) {cerr << x << endl;}
template<typename T, typename ...S> void _do(T && x, S&&...y) {cerr << x << ", "; _do(y...);}
#else
#define bug(...) 826
#endif
template<typename T> void print(T && x) {cout << x << "\n";}
template<typename T, typename... S> void print(T && x, S&&... y) {cout << x << ' ';print(y...);}

const int Mod=1000000007,Mod2=998244353;
const int MOD=Mod2;
const int maxn=100005;

//i_am_noob
#define wiwihorz  
int n,k,a[maxn],val[490][490];
vector<pii> vec;

void orzck(){
    cin >> n >> k;
    rep(k) cin >> a[i];
    int x=max_element(a,a+k)-a;
    int m=0;
    rep2(i,1,4949){
        if(i*i-(i/2)*(i/2)>=n&&i*((i+1)/2)>=a[x]){
            m=i;
            break;
        }
    }
    vec.clear();
    rep(m) if(i%2==0) rep1(j,m) if(j%2==1) vec.pb({i,j});
    rep(m) if(i%2==0) rep1(j,m) if(j%2==0) vec.pb({i,j});
    rep(m) if(i%2==1) rep1(j,m) if(j%2==0) vec.pb({i,j});
    rep(m) rep1(j,m) val[i][j]=0;
    int cur=0;
    rep(a[x]) val[vec[cur].first][vec[cur].second]=x+1,cur++;
    rep(k) if(i!=x) rep1(j,a[i]) val[vec[cur].first][vec[cur].second]=i+1,cur++;
    print(m);
    rep(m){
        rep1(j,m) print0(val[i][j]);
        cout << "\n";
    }
}

signed main(){
    ios_base::sync_with_stdio(0),cin.tie(0);
    #ifdef i_am_noob
    freopen("input1.txt","r",stdin);
    freopen("output1.txt","w",stdout);
    freopen("output2.txt","w",stderr);
    #endif
    cout << fixed << setprecision(15);
    int t;
    #ifdef wiwihorz
    cin >> t;
    #else
    t=1;
    #endif
    while(t--) orzck();
    return 0;
}