Given an array A of integers, return the number of (contiguous, non-empty) subarrays that have a sum divisible by K.
 

Example 1:
Input: A = [4,5,0,-2,-3,1], K = 5
Output: 7
Explanation: There are 7 subarrays with a sum divisible by K = 5:
[4, 5, 0, -2, -3, 1], [5], [5, 0], [5, 0, -2, -3], [0], [0, -2, -3], [-2, -3]

 
Note:

1 <= A.length <= 30000
-10000 <= A[i] <= 10000
2 <= K <= 10000

```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 subarraysDivByK(self, A: List[int], K: int) -> int:\n        prefix_sum = [0]\n        for idx, i in enumerate(A):\n            prefix_sum.append(i+prefix_sum[idx])\n        print(prefix_sum)\n        \n        # now we go through and try to see if we've seen the pair number already\n        \n        num_enc = dict()\n        total = 0\n        for i in prefix_sum:\n            if (i%K) in num_enc:\n                total+=num_enc[i%K]\n            if (i%K - K) in num_enc:\n                total+=num_enc[i%K - K]\n            if i%K not in num_enc:\n                num_enc[i%K] = 0\n            num_enc[i%K]+=1\n        return total\n            \n            \n                \n\n        \n#         total = 0\n#         for i in range(0, len(A)):\n#             curr_sum = A[i]\n#             if curr_sum%K==0:\n#                 total+=1\n#             for j in range(i+1, len(A)):\n#                 curr_sum+=A[j]\n#                 if curr_sum%K==0:\n#                     total+=1\n#         return total\n                \n                \n                \n                \n                \n#         for wsize in range(1, len(A)):\n#             i = 0\n#             curr_sum = sum(A[j] for j in range(0, wsize+1))\n#             while i + wsize < len(A):\n                \n#                 if i != 0:\n#                     curr_sum-=A[i-1]\n#                     curr_sum+=A[i+wsize]\n#                 if curr_sum%5==0:\n#                     total+=1\n#                 print(i, i+wsize, wsize, curr_sum)\n#                 i+=1\n#         return total\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'subarraysDivByK'
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: 6200