“Jesse, you asked me if I was in the meth business, or the money business… Neither. I’m in the empire business.”
Walter’s sold his stack in Gray Matter Technologies, a company which he deserved half a credit, for peanuts. Now this company is worth a billion dollar company. Walter wants to get it's shares to have his Empire Business back and he founds an opportunity.  
There are $N$ persons having shares $A_1, A_2, A_3, … A_N$ in this company. Walter can buy these shares with their minimum Sold Values. 
Sold Values of a person's share $ i $ $(1 \leq i \leq N) $ with another person's share $ j $ $ (1 \leq j \leq N) $ is equal to $ A_j+|i-j| $. So, a person's share can have $ N $ possible sold values and Walter has to find minimum sold value among them for each person.
Since Walter has to run his meth business also he asks you to find minimum sold value for each person.

-----Input:-----
- First line will contain $T$, number of test cases. Then the testcases follow. 
- The First line of each test case contains a integer $N$.
- The Second line of each test case contains $N$ space integers namely $A_1,A_2,…A_N$.

-----Output:-----
For each test case, output in single line $N$ space integers denoting minimum sold value for each person.

-----Constraints-----
- $1 \leq T \leq 10^5$
- $1 \leq N \leq 2*10^6 $
- $1 \leq A_i \leq 10^9 $
Sum of $N$ over all test cases will not exceed $2*10^6$.

-----Sample Input:-----
2
5
6 5 5 5 2
5
1 2 3 4 5

-----Sample Output:-----
6 5 4 3 2
1 2 3 4 5

-----Explanation-----
For first case:
- Sold value for index $1$:  $6,6,7,8,6$
- Sold value for index $2$:  $7,5,6,7,5$
- Sold value for index $3$:  $8,6,5,6,4$
- Sold value for index $4$:  $9,7,6,5,3$
- Sold value for index $5$:  $10,8,7,6,2$
Minimum sold value for each index will be $6,5,4,3,2$.

```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 itertools import accumulate, count\nfrom operator import add, sub\n\nf = lambda x: accumulate(list(map(sub, x, count())), min)\n\nfor s in [*open(0)][2::2]:\n a = *list(map(int, s.split())),\n n = len(a)\n b = f(a)\n c = reversed([*f(reversed(a))])\n print(*(list(map(min, list(map(add, b, count())), list(map(sub, c, count(1 - n)))))))\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 19702