Chef wants to teach a lesson of sharing to the students.
There are $N$ students (numbered from $1$ to $N$ from left to right) who are asked to stand in a row. Initially Chef gave $A$$i$ candies to the $i$$th$ child. In one operation any child can give any number of candies to the child standing to his immediate left (i.e. $i$$th$ child can give any amount of candies to the $(i-1)$$th$ child. In particular 1st child cannot give his candies to anyone).  
He asked them to minimize the maximum value of candies a student can possess after performing any number of operations (possibly zero). 
Help the students finding such maximum value.

-----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.
- First line of each test case contains a single integer $N$ denoting the number of students.
- Second line contains $N$ space-separated integers $A$$1$,$A$$2$,$.....$ $A$$N$ denoting the initial amount of candies chef gave to them.

-----Output:-----
- For each test case, print a single line containing one integer ― maximum value after sharing.

-----Constraints-----
- $1 \leq T \leq 100$
- $1 \leq N \leq 10^5$
- $0$ $\leq$ $A$$i$ $\leq$ $10^9$
- Sum of $N$ over all Test Cases does not exceed $10^5$

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

-----Sample Output-----
3 
5  

-----Explanation-----
- 
For First Test Case:
The $5$$th$ student will give $2$ candies to $4$$th$ student and $4$$th$ will give $3$ candies to $3$$rd$ and $3$$rd$ will give $3$ candies to $2$$nd$ and $2$$nd$ will give $2$ candies to $1$$st$. So finally the number of candies that they will have are 
$[3,3,3,3,3]$ and the value of maximum candies is $3$.
- 
For Second Test Case:
Sharing to the left student will not change the maximum value as $1$$st$ cannot share to anyone. So the maximum value will remain $5$.

```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 = 'import math\nT=int(input())\n\nfor _ in range(T):\n N=int(input())\n A=list(map(int,input().split()))\n ans=0\n left=0\n for i in range(N):\n  v=A[i]-ans-left\n  if (v<0):\n   left=-v\n  else:\n   ans=ans+math.ceil(v/(i+1))\n   left=(math.ceil(v/(i+1))*(i+1))-v\n  \n  \n print(ans)\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13163