Chef likes to play with array elements. His teacher has given him an array problem. But now he is busy as Christmas is coming. So, he needs your help. Can you help him to solve this problem.
You are given an array $(A1,A2,A3……AN)$ of length $N$. You have to create an another array using the given array in the following ways:

For each valid i, the ith element of the output array will be the sum of the ith element and (A[i])th element if $A[i]$ is less equal $N$.

Other wise for each valid i following the step below

i) Divide the value of $A[i]$ by 2 untill it will be less than$N$.

ii) then find the difference ($D$) between $N$ and $A[i]$.

iii) the ith element of the output array will be $Dth$ element.  

-----Input:-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of T test cases follows.  
- The first line of each test case contains a single integer $N$.  
- The second line contains $N$ space-separated integers $A1,A2,…,AN$.   

-----Output:-----
- For each testcase, print new array in each line.

-----Constraints-----
- $1 \leq T \leq 1000$
- $1 \leq N \leq 10^5$
- $1\leq A1,A2.....AN \leq 10^7$

-----Sample Input:-----
2

5

2 4 5 7 9

4

5 4 2 3

-----Sample Output:-----
6 11 14 4 2

4 7 6 5

-----EXPLANATION:-----
For 1st test case: A1 = 2+4 =6, A2 = 4+7 =11 , A3 = 5+9 =14 , A4 > N (5) ,So A4/2 = 3 then A4 = A[5 -3] , A4=A[2]=4, And A5 =A[1]=2. Then array becomes 6,11,14,4,2.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "from sys import stdin\r\nfor _ in range(int(stdin.readline().strip())) :\r\n    n = int(stdin.readline().strip())\r\n    a = list(map(int,stdin.readline().split()))\r\n    b = []\r\n    for i,ch in enumerate(a) :\r\n        if ch <= n :\r\n            b.append(ch+a[ch-1])\r\n        else :\r\n            while ch >= n :\r\n                ch//=2\r\n            d = n-ch-1\r\n            b.append(a[d])\r\n    print(' '.join(map(str,b)))\r\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13429