Given an array of integers nums and an integer k. A continuous subarray is called nice if there are k odd numbers on it.
Return the number of nice sub-arrays.
 
Example 1:
Input: nums = [1,1,2,1,1], k = 3
Output: 2
Explanation: The only sub-arrays with 3 odd numbers are [1,1,2,1] and [1,2,1,1].

Example 2:
Input: nums = [2,4,6], k = 1
Output: 0
Explanation: There is no odd numbers in the array.

Example 3:
Input: nums = [2,2,2,1,2,2,1,2,2,2], k = 2
Output: 16

 
Constraints:

1 <= nums.length <= 50000
1 <= nums[i] <= 10^5
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 = 'class Solution:\n    def numberOfSubarrays(self, nums: List[int], k: int) -> int:\n        if len(nums)==0:\n            return 0\n        preprocess = [0] * (len(nums) + 1) # preprocess[k] = num odd numbers in nums[:k]\n        count = 0\n        for i in range(len(nums)):\n            if nums[i] % 2 == 1:\n                count+=1\n            preprocess[i+1] = count\n        print(preprocess)\n        cont_preprocess = [preprocess[0]]\n        counts_cont = [1]\n        last_el = preprocess[0]\n        for i in range(1, len(preprocess)):\n            if preprocess[i] == last_el:\n                counts_cont[-1] += 1\n            else:\n                last_el = preprocess[i]\n                cont_preprocess.append(last_el)\n                counts_cont.append(1)\n        result=0\n        # number of (i<j) where a[j]-a[i] == k\n        left_cursor = 0\n        right_cursor = 0\n        while left_cursor < len(cont_preprocess):\n            diff = cont_preprocess[right_cursor] - cont_preprocess[left_cursor]\n            if diff < k:\n                right_cursor += 1\n            elif diff == k:\n                result += (counts_cont[right_cursor] * counts_cont[left_cursor])\n                right_cursor += 1\n            else:\n                left_cursor += 1\n            if right_cursor == len(cont_preprocess):\n                right_cursor = len(cont_preprocess) - 1\n                left_cursor += 1\n        return result'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'numberOfSubarrays'
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: 6649