Given an array of integers arr of even length n and an integer k.
We want to divide the array into exactly n / 2 pairs such that the sum of each pair is divisible by k.
Return True If you can find a way to do that or False otherwise.
 
Example 1:
Input: arr = [1,2,3,4,5,10,6,7,8,9], k = 5
Output: true
Explanation: Pairs are (1,9),(2,8),(3,7),(4,6) and (5,10).

Example 2:
Input: arr = [1,2,3,4,5,6], k = 7
Output: true
Explanation: Pairs are (1,6),(2,5) and(3,4).

Example 3:
Input: arr = [1,2,3,4,5,6], k = 10
Output: false
Explanation: You can try all possible pairs to see that there is no way to divide arr into 3 pairs each with sum divisible by 10.

Example 4:
Input: arr = [-10,10], k = 2
Output: true

Example 5:
Input: arr = [-1,1,-2,2,-3,3,-4,4], k = 3
Output: true

 
Constraints:

arr.length == n
1 <= n <= 10^5
n is even.
-10^9 <= arr[i] <= 10^9
1 <= k <= 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 canArrange(self, arr: List[int], k: int) -> bool:\n        # int arr and integer k\n        # divide array into pairs such that the sum of each pair is divisible by k\n        # return True if possible, other false\n        \n        # [1, 2, 3, 4, 5, 10, 6, 7, 8, 9] k = 5   5, 10, 15, 20, 25, 30\n        #  4  3  2\n        #  9  8  7\n        # 14 13 12\n        # elem = 1 poss: 4, 9 k%5 == 4  \n        # elem = 2 poss: 3, 8 k%5 == 3\n        # elem = 3 poss: 2, 7 k%5 == 2\n        # elem = 4 poss: 1, 6 k%5 == 1\n        # elem = 5 poss: 10   k%5 == 0\n        # elem = 6 poss: 4, 9\n        # elem = 7 poss: 3, 8 # see if there are any pairs that have not been matched yet. if so, check their possible matches and see if one is available\n        # elem = 8 poss: 2, 7\n        # elem = 9 poss: 1, 6\n        # elem = 10 poss: 5\n        \n        # arr = [1,2,3,4,5,6], k = 10\n        # elem = 1 poss: x\n        \n        \n        # 1 - 4 6 - 9 \n        # 1 - 9 4 - 6\n        \n        # 2 - 3 8 - 7 \n        # 2 - 8 3 - 7\n        \n        # 5 - 10\n        modFrequencies = {}\n        for i in range(0, len(arr)):\n            difference = arr[i] % k\n            if difference not in modFrequencies:\n                modFrequencies[difference] = 0\n            modFrequencies[difference] += 1\n            \n        for mod in modFrequencies:\n            if mod == 0:\n                if modFrequencies[mod] % 2 == 1: \n                    return False\n            elif k-mod not in modFrequencies or modFrequencies[mod] != modFrequencies[k-mod]:\n                return False\n        return True\n            \n            \n            \n        \n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'canArrange'
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