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:
/**
 * Created by Himanshu
 **/

import java.util.*;
import java.io.*;
import java.math.*;

public class B1501 {
    public static void main(String[] args) throws IOException {
        PrintWriter out = new PrintWriter(System.out);
        Reader s = new Reader();
        int t = s.i();
        while (t-- > 0) {
            int n = s.i();
            int [] arr = s.arr(n);
            int [] a = new int[n+1];
            for (int i=0;i<n;i++) {
                if (arr[i] != 0) {
                    a[i+1]--;
                    a[Math.max(0,i+1-arr[i])] ++;
                }
            }
            for (int i=1;i<=n;i++) {
                a[i] += a[i-1];
            }
            for (int i=0;i<n;i++) {
                int x = a[i];
                if (x == 0) out.print("0 ");
                else out.print("1 ");
            }
            out.println();
        }
        out.flush();
    }

    public static void shuffle(long[] arr) {
        int n = arr.length;
        Random rand = new Random();
        for (int i = 0; i < n; i++) {
            long temp = arr[i];
            int randomPos = i + rand.nextInt(n - i);
            arr[i] = arr[randomPos];
            arr[randomPos] = temp;
        }
    }

    private static int gcd(int a, int b) {
        if(b == 0) return a;
        return gcd(b,a%b);
    }

    public static long nCr(long[] fact, long[] inv, int n, int r, long mod) {
        if (n < r)
            return 0;
        return ((fact[n] * inv[n - r]) % mod * inv[r]) % mod;
    }

    private static void factorials(long[] fact, long[] inv, long mod, int n) {
        fact[0] = 1;
        inv[0] = 1;
        for (int i = 1; i <= n; ++i) {
            fact[i] = (fact[i - 1] * i) % mod;
            inv[i] = power(fact[i], mod - 2, mod);
        }
    }

    private static long power(long a, long n, long p) {
        long result = 1;
        while (n > 0) {
            if (n % 2 == 0) {
                a = (a * a) % p;
                n /= 2;
            } else {
                result = (result * a) % p;
                n--;
            }
        }
        return result;
    }

    private static long power(long a, long n) {
        long result = 1;
        while (n > 0) {
            if (n % 2 == 0) {
                a = (a * a);
                n /= 2;
            } else {
                result = (result * a);
                n--;
            }
        }
        return result;
    }

    private static long query(long[] tree, int in, int start, int end, int l, int r) {
        if (start >= l && r >= end) return tree[in];
        if (end < l || start > r) return 0;
        int mid = (start + end) / 2;
        long x = query(tree, 2 * in, start, mid, l, r);
        long y = query(tree, 2 * in + 1, mid + 1, end, l, r);
        return x + y;
    }

    private static void update(int[] arr, long[] tree, int in, int start, int end, int idx, int val) {
        if (start == end) {
            tree[in] = val;
            arr[idx] = val;
            return;
        }
        int mid = (start + end) / 2;
        if (idx > mid) update(arr, tree, 2 * in + 1, mid + 1, end, idx, val);
        else update(arr, tree, 2 * in, start, mid, idx, val);
        tree[in] = tree[2 * in] + tree[2 * in + 1];
    }

    private static void build(int[] arr, long[] tree, int in, int start, int end) {
        if (start == end) {
            tree[in] = arr[start];
            return;
        }
        int mid = (start + end) / 2;
        build(arr, tree, 2 * in, start, mid);
        build(arr, tree, 2 * in + 1, mid + 1, end);
        tree[in] = (tree[2 * in + 1] + tree[2 * in]);
    }

    static class Reader {
        private InputStream mIs;
        private byte[] buf = new byte[1024];
        private int curChar, numChars;

        public Reader() {
            this(System.in);
        }

        public Reader(InputStream is) {
            mIs = is;
        }

        public int read() {
            if (numChars == -1) throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = mIs.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public String s() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public long l() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int i() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public double d() throws IOException {
            return Double.parseDouble(s());
        }

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

        public int[] arr(int n) {
            int[] ret = new int[n];
            for (int i = 0; i < n; i++) {
                ret[i] = i();
            }
            return ret;
        }

        public long[] arrLong(int n) {
            long[] ret = new long[n];
            for (int i = 0; i < n; i++) {
                ret[i] = l();
            }
            return ret;
        }
    }
//    static class pairLong implements Comparator<pairLong> {
//        long first, second;
//
//        pairLong() {
//        }
//
//        pairLong(long first, long second) {
//            this.first = first;
//            this.second = second;
//        }
//
//        @Override
//        public int compare(pairLong p1, pairLong p2) {
//            if (p1.first == p2.first) {
//                if(p1.second > p2.second) return 1;
//                else return -1;
//            }
//            if(p1.first > p2.first) return 1;
//            else return -1;
//        }
//    }
//    static class pair implements Comparator<pair> {
//        int first, second;
//
//        pair() {
//        }
//
//        pair(int first, int second) {
//            this.first = first;
//            this.second = second;
//        }
//
//        @Override
//        public int compare(pair p1, pair p2) {
//            if (p1.first == p2.first) return p1.second - p2.second;
//            return p1.first - p2.first;
//        }
//    }
}