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 JAVA):

Solution:
/* Author : ᴅᴇʙᴏᴊʏᴏᴛɪ ᴍᴀɴᴅᴀʟ
Attribute : Some of the methods are copied from GeeksforGeeks Website  */
import java.util.*;
import java.lang.*;
import java.io.*;
public class Main
{ 
  static  Reader sc=new Reader();
  // static FastReader sc=new FastReader(System.in);
  
 public static void main (String[] args) throws java.lang.Exception
   {
	try{
	    /*
	        int n=sc.nextInt();
	        ArrayList<Integer> al=new ArrayList<>();
	        ArrayList<Long> al=new ArrayList<>();
	        Set<Integer> set=new HashSet<>();
	        Collections.sort(al,Collections.reverseOrder());
	     
	        long n=sc.nextLong();
	        for(int i=0;i<n;i++) 
	        String s=sc.next();
	     */
		  int t = sc.nextInt();
		  while(t-->0)
		    { 
		       int n=sc.nextInt();
		       
		       int a[]=new int[n];
		       for(int i=0;i<n;i++)
		         {
		           a[i]=sc.nextInt();
		         }
		      int ans[]=new int[n];
		      Arrays.fill(ans,0);
		      int cur=0;
		      for(int i=n-1;i>=0;i--)
              {
                int ele=a[i];
                cur=Math.max(ele,cur);
                if(cur>0) 
                  {
                     ans[i]=1;
                     cur--;
                  }
              }
            print(ans);
		     // out.println( );
		    }
	     out.flush();
	     out.close();
	   }     
	catch(Exception e)
		 {}
	}
 
 /*
  ....sᴏʟᴜᴛɪᴏɴ  ᴇɴᴅs  ʜᴇʀᴇ !!!!!!!! sᴏʟᴜᴛɪᴏɴ  ᴇɴᴅs  ʜᴇʀᴇ.... 
 */
  
 /*                     
    Map<Long,Long> map=new HashMap<>();
             for(int i=0;i<n;i++)
               {
                  if(!map.containsKey(a[i]))
                   map.put(a[i],1);
                 else
                   map.replace(a[i],map.get(a[i])+1);
               }
     
    Set<Map.Entry<Long,Long>> hmap=map.entrySet();
             for(Map.Entry<Long,Long> data : hmap)
               {
          
               }
       
   Iterator<Integer> it = set.iterator();
          while(it.hasNext()) 
           { 
            int x=it.next();
           }
   */
static void flag(boolean flag)
   {
       out.println(flag ? "YES" : "NO");
       out.flush();
   }

static void print_int(ArrayList<Integer> al)
  {
     int si=al.size();
     for(int i=0;i<si;i++)
       {
          out.print(al.get(i)+" ");
       }
     out.println();
     out.flush();
  }
static void print_long(ArrayList<Long> al)
  {
     int si=al.size();
     for(int i=0;i<si;i++)
       {
          out.print(al.get(i)+" ");
       }
     out.println();
     out.flush();
  }
static void print(int a[])
  {
     int n=a.length;
     for(int i=0;i<n;i++)
       {
          out.print(a[i]+" ");
       }
     out.println();
     out.flush();
  }
static void print(long a[])
  {
     int n=a.length;
     for(int i=0;i<n;i++)
       {
          out.print(a[i]+" ");
       }
     out.println();
     out.flush();
  } 

static class Graph
  {
        int v;
        ArrayList<Integer> list[];
        Graph(int v)
        {
            this.v=v;
            list=new ArrayList[v+1];
            for(int i=1;i<=v;i++)
                list[i]=new ArrayList<Integer>();
        }
        void addEdge(int a, int b)
        {
            this.list[a].add(b);
        }
    }
static void DFS(Graph g, boolean[] visited, int u)
	{
        visited[u]=true;
        int v=0;
        for(int i=0;i<g.list[u].size();i++)
        {
            v=g.list[u].get(i);
            if(!visited[v])
               DFS(g,visited,v);
        }
  } 
  
static class Pair
   {
      int x,y;
      Pair(int x,int y)
       {
          this.x=x;
          this.y=y;
       }
   }
   
static long sum_array(int a[])
 {
    int n=a.length;
    long sum=0;
    for(int i=0;i<n;i++)
     sum+=a[i];
    return sum;
 }
static long sum_array(long a[])
 {
    int n=a.length;
    long sum=0;
    for(int i=0;i<n;i++)
     sum+=a[i];
    return sum;
 }

 static void sort(int[] a) 
   {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}
static void sort(long[] a) 
   {
		ArrayList<Long> l=new ArrayList<>();
		for (long i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}

static void reverse_array(int a[])
 {
    int n=a.length;
    int i,t; 
    for (i = 0; i < n / 2; i++) { 
            t = a[i]; 
            a[i] = a[n - i - 1]; 
            a[n - i - 1] = t; 
        } 
 }
static void reverse_array(long a[])
 {
    int n=a.length;
    int i; long t; 
    for (i = 0; i < n / 2; i++) { 
            t = a[i]; 
            a[i] = a[n - i - 1]; 
            a[n - i - 1] = t; 
        } 
 }
 
static long gcd(long a, long b) 
    { 
        if (a == 0) 
            return b; 
          
        return gcd(b%a, a); 
    } 
static int gcd(int a, int b) 
    { 
        if (a == 0) 
            return b; 
          
        return gcd(b%a, a); 
    } 

   static class FastReader{
 
        byte[] buf = new byte[2048];
        int index, total;
        InputStream in;
 
        FastReader(InputStream is) {
            in = is;
        }
 
        int scan() throws IOException {
            if (index >= total) {
                index = 0;
                total = in.read(buf);
                if (total <= 0) {
                    return -1;
                }
            }
            return buf[index++];
        }
 
        String next() throws IOException {
            int c;
            for (c = scan(); c <= 32; c = scan());
            StringBuilder sb = new StringBuilder();
            for (; c > 32; c = scan()) {
                sb.append((char) c);
            }
            return sb.toString();
        }
 
        int nextInt() throws IOException {
            int c, val = 0;
            for (c = scan(); c <= 32; c = scan());
            boolean neg = c == '-';
            if (c == '-' || c == '+') {
                c = scan();
            }
            for (; c >= '0' && c <= '9'; c = scan()) {
                val = (val << 3) + (val << 1) + (c & 15);
            }
            return neg ? -val : val;
        }
 
        long nextLong() throws IOException {
            int c;
            long val = 0;
            for (c = scan(); c <= 32; c = scan());
            boolean neg = c == '-';
            if (c == '-' || c == '+') {
                c = scan();
            }
            for (; c >= '0' && c <= '9'; c = scan()) {
                val = (val << 3) + (val << 1) + (c & 15);
            }
            return neg ? -val : val;
        }
    }
   
    static class Reader 
    { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[64]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9'); 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
  
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
  
            if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
  
        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 
  
        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    }
  static  PrintWriter out=new PrintWriter(System.out);
  static int int_max=Integer.MAX_VALUE;
  static int int_min=Integer.MIN_VALUE;
  static long long_max=Long.MAX_VALUE;
  static long long_min=Long.MIN_VALUE;
}
// Thank You !