Given an array of integers nums and a positive integer k, find whether it's possible to divide this array into sets of k consecutive numbers
Return True if its possible otherwise return False.
 
Example 1:
Input: nums = [1,2,3,3,4,4,5,6], k = 4
Output: true
Explanation: Array can be divided into [1,2,3,4] and [3,4,5,6].

Example 2:
Input: nums = [3,2,1,2,3,4,3,4,5,9,10,11], k = 3
Output: true
Explanation: Array can be divided into [1,2,3] , [2,3,4] , [3,4,5] and [9,10,11].

Example 3:
Input: nums = [3,3,2,2,1,1], k = 3
Output: true

Example 4:
Input: nums = [1,2,3,4], k = 3
Output: false
Explanation: Each array should be divided in subarrays of size 3.

 
Constraints:

1 <= nums.length <= 10^5
1 <= nums[i] <= 10^9
1 <= k <= nums.length

```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 = "\n# Mai Trinh\n# COSC 6320 - Data Structures and Algorithm\n# Instructor: Gopal Pandurangan\n# Divides array in sets of k consecutive numbers.\n\n# ----------------------\n# Given an array of integers nums and a positive integer k, find whether it's possible to divide this array into sets of k consecutive numbers.\n# Return True if its possible otherwise return False.\n# ----------------------\ndef isPossibleDivide(nums, k):\n    if (len(nums) % k != 0): #if the size of arrays is not divisible by k, cannot have sets of k numbers\n        return False\n    else:\n        nums.sort() #sort array\n        return decreaseConquer(nums, k) #calling the decrease/conquer algorihtm with the sorted array.\n\n#Decrease-Conquer algorithm to determine if array can be divide into sets of k consecutive numbers\ndef decreaseConquer(A, k):\n    if (len(A) == 0): #base case\n        return True\n    else: #recursive\n        pivot= A[len(A) - 1] #choose the last element (the largest element) in array\n        for i in range(k): #search for k consecutives in correspond to the largest number\n            j = binarySearch(A, 0, len(A)-1, pivot-i) #use binary search to find p-1, p-2,.., p-(k-1)\n            if (j == -1): #if element is not found in the array, there is no k consecutive numbers\n                return False\n            else: #if found, remove the element from array\n                del A[j]\n        #array is reduced in size (n - k), recursively calling decreaseConquer algorithm with the updated array\n        return decreaseConquer(A, k)\n\n#Search for specific element in the array - O(log n)\ndef binarySearch (S, l, r, x): \n    if l <= r: \n        mid = l + (r - l) // 2 #find the middle element\n\n        if S[mid] == x: # If element is the middle element\n            return mid \n\n        elif S[mid] > x: #if element is in the left subarray\n            return binarySearch(S, l, mid-1, x) \n\n        else: #if element is in the right subarray\n            return binarySearch(S, mid + 1, r, x) \n\n    else: # Element is not present in the array \n        return -1\n    \nA = [1,2,3,3,4,4,5,6]\nk = 4\nans = isPossibleDivide(A, k)\n\nprint(ans)\nclass Solution:\n    def isPossibleDivide(self, nums: List[int], k: int) -> bool:\n        return isPossibleDivide(nums, k)"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'isPossibleDivide'
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: 6594