In a given integer array A, we must move every element of A to either list B or list C. (B and C initially start empty.)
Return true if and only if after such a move, it is possible that the average value of B is equal to the average value of C, and B and C are both non-empty.
Example :
Input: 
[1,2,3,4,5,6,7,8]
Output: true
Explanation: We can split the array into [1,4,5,8] and [2,3,6,7], and both of them have the average of 4.5.

Note:

The length of A will be in the range [1, 30].
A[i] will be in the range of [0, 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 splitArraySameAverage(self, A: List[int]) -> bool:\n    def splitArraySameAverage(self, A: List[int]) -> bool:\n\n    # A subfunction that see if total k elements sums to target\n    # target is the goal, k is the number of elements in set B, i is the index we have traversed through so far\n        mem = {}\n\n        def find(target, k, i):\n        # if we are down searching for k elements in the array, see if the target is 0 or not. This is a basecase\n            if k == 0: return target == 0\n\n            # if the to-be selected elements in B (k) + elements we have traversed so far is larger than total length of A\n            # even if we choose all elements, we don't have enough elements left, there should be no valid answer.\n            if k + i > len(A): return False\n\n            if (target, k, i) in mem: return mem[(target, k, i)]\n\n            # if we choose the ith element, the target becomes target - A[i] for total sum\n            # if we don't choose the ith element, the target doesn't change\n            mem[(target - A[i], k - 1, i + 1)] = find(target - A[i], k - 1, i + 1) or find(target, k, i + 1)\n\n            return mem[(target - A[i], k - 1, i + 1)]\n\n        n, s = len(A), sum(A)\n    # Note that the smaller set has length j ranging from 1 to n//2+1\n    # we iterate for each possible length j of array B from length 1 to length n//2+1\n    # if s*j%n, which is the sum of the subset, it should be an integer, so we only proceed to check if s * j % n == 0\n    # we check if we can find target sum s*j//n (total sum of j elements that sums to s*j//n)\n        return any(find(s * j // n, j, 0) for j in range(1, n // 2 + 1) if s * j % n == 0)\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'splitArraySameAverage'
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: 8622