Problem: This week Arkady wanted to cook some pancakes (to follow ancient traditions) and make a problem about that. But then he remembered that one can't make a problem about stacking pancakes without working at a specific IT company, so he decided to bake the Napoleon cake instead.

To bake a Napoleon cake, one has to bake n dry layers first, and then put them on each other in one stack, adding some cream. Arkady started with an empty plate, and performed the following steps n times: 

  * place a new cake layer on the top of the stack; 
  * after the i-th layer is placed, pour a_i units of cream on top of the stack. 



When x units of cream are poured on the top of the stack, top x layers of the cake get drenched in the cream. If there are less than x layers, all layers get drenched and the rest of the cream is wasted. If x = 0, no layer gets drenched.

<image> The picture represents the first test case of the example.

Help Arkady determine which layers of the cake eventually get drenched when the process is over, and which don't.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 20 000). Description of the test cases follows.

The first line of each test case contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of layers in the cake.

The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ n) — the amount of cream poured on the cake after adding each layer.

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case, print a single line with n integers. The i-th of the integers should be equal to 1 if the i-th layer from the bottom gets drenched, and 0 otherwise.

Example

Input


3
6
0 3 0 0 1 3
10
0 0 0 1 0 5 0 0 0 2
3
0 0 0


Output


1 1 0 1 1 1 
0 1 1 1 1 1 0 0 1 1 
0 0 0 

Solution (in CPP):

Solution:
#include <iostream>
#include <bits/stdc++.h>
using namespace std;
typedef long long  l;
#define fastIO              ios::sync_with_stdio(false), cin.tie(0)
#define pf                  push_front
#define pb                  push_back
#define popb                pop_back()
#define popf                pop_front()
#define loop(i,n)           for(int i=0;i<n;i++)
#define loope(i,n)           for(int i=0;i<=n;i++)
#define loop1(i,n)           for(int i=1;i<n;i++)
#define loop1e(i,n)           for(int i=1;i<=n;i++)
#define loops(i,x,n)        for(int i=x;i<n;i++)
#define loopr(i,n)          for(int i=n-1;i>=0;i--)
#define loop1e(i,n)          for(int i=1;i<=n;i++)
#define F first
#define S second
#define LB lower_bound
#define UB upper_bound
#define vc vector
#define vll vector<long long>
#define pll pair<long long,long long>
#define eb emplace_back
#define pb push_back
//#define mp make_pair
#define INT_BITS 32
// #define  st                  l t; cin>>t;
#define  sn                  l n; cin>>n;
#define all(x) x.begin(),x.end()
//#define  unordered_map<l,l>  u;
#define MOD1 1000000007
bool cmp(pair<string,l>&a,pair<string,l>&b)
{
    return(a.first<b.first);
    
}
l ce(l a , l b)
{
    if(a%b==0)
        return a/b;
    return(a/b)+1;
}
int main()
{
  #ifndef ONLINE_JUDGE
      //for getting input from input.txt
      freopen("input.txt","r",stdin);
      //for writing output to output.txt
      freopen("output1.txt","w",stdout);
      #endif
    
      l t;
      cin>>t;
      while(t--)
      { l n;
        cin>>n;
        l cpy = n;
        l a[n];
       
        for(l i=0;i<n;i++)
        {
            cin>>a[i];
            // cin>>b[i];
        }
        l ans[n],k=0;
        for(l i=n-1;i>=0;i--)
        {
            if(a[i]>0)
            {
                if(a[i]>k)
                {
                    k = a[i]-1;
                    ans[i]=1;
                }
                else
                {
                    k--;
                    ans[i]=1;
                }
                
            }
            else
            {
                if(k>0){
                    ans[i]=1;
                    k--;
                }
                else
                    ans[i]=0;
            }
        }
        loop(i,n)
        cout<<ans[i]<<" ";
        cout<<endl;
       

        
      }
return 0;
        
}