Given an integer array arr and a target value target, return the integer value such that when we change all the integers larger than value in the given array to be equal to value, the sum of the array gets as close as possible (in absolute difference) to target.
In case of a tie, return the minimum such integer.
Notice that the answer is not neccesarilly a number from arr.
 
Example 1:
Input: arr = [4,9,3], target = 10
Output: 3
Explanation: When using 3 arr converts to [3, 3, 3] which sums 9 and that's the optimal answer.

Example 2:
Input: arr = [2,3,5], target = 10
Output: 5

Example 3:
Input: arr = [60864,25176,27249,21296,20204], target = 56803
Output: 11361

 
Constraints:

1 <= arr.length <= 10^4
1 <= arr[i], target <= 10^5

```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

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "class Solution:\n    def findBestValue(self, arr: List[int], target: int) -> int:\n        #brute force, linear scan, TIME LIMIT EXCEEDED\n        '''\n        sums = []\n        for i in range(max(arr)+1):\n            currSum = 0 \n            for val in arr: \n                if val > i: \n                    currSum += i\n                else:\n                    currSum += val\n            \n            sums.append((abs(currSum-target),i))\n        sums.sort(key = lambda x:x[0])\n        return sums[0][1]\n        '''\n        \n        #linear scan with stopping condition, works! but really bad lol \n        '''\n        sums = []\n        for i in range(max(arr)+1):\n            currSum = 0 \n            for val in arr: \n                if val > i: \n                    currSum += i\n                else:\n                    currSum += val\n            if currSum-target > 0:\n                sums.append((abs(currSum-target),i))\n                break\n            else:\n                sums.append((abs(currSum-target),i))\n        sums.sort(key = lambda x:x[0])\n        return sums[0][1]\n        '''\n        \n        #binary search, find the minimum integer that meets stopping condition\n        #since you are trying to minimize the difference, stop on the smallest one and find the corresponding value \n        '''\n        def condition(cutoff): \n            currSum = 0\n            for val in arr: \n                if val > cutoff: \n                    currSum += cutoff\n                else:\n                    currSum += val\n            return abs(currSum - target)\n            \n        left, right = 0, target\n        currSum = (float('inf'), -1) #smallest sum, the cutoff value which gives you the smallest sum \n        while left <= right: \n            mid = left + (right - left) // 2\n            checkSum = condition(mid)\n            if checkSum < currSum[0]: #if the smallest sum is smaller than the previous smallest sum, store the cutoff value\n                currSum = (checkSum, mid)\n                right = mid - 1\n            else:\n                left = mid + 1\n            print(left, right)\n        return currSum[1]\n        '''\n        #binary search but look for the cutoff point\n        def condition(cutoff): \n            currSum = 0\n            for val in arr: \n                if val > cutoff: \n                    currSum += cutoff\n                else:\n                    currSum += val\n            return currSum   \n        \n        left, right = 0, max(arr)\n        while left < right: \n            mid = left + (right - left) // 2\n            if condition(mid) < target:\n                left = mid + 1\n            else:\n                right = mid \n\n        if abs(target-condition(left)) < abs(target-condition(left-1)): \n            return left\n        else:\n            return left - 1\n        \n        \n        \n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'findBestValue'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 5592