A stick is balanced horizontally on a support. Will it topple over or stay balanced? (This is a physics problem: imagine a real wooden stick balanced horizontally on someone's finger or on a narrow table, for example). 

The stick is represented as a list, where each entry shows the mass in that part of the stick.

The stick is balanced on a support. The "terrain" is represented by a list of 1s and 0s, where the 1s represent the support and the 0s represent empty space. Each index is a coordinate on the x-axis, so e.g. the physical interpretations of some terrains are as follows:

![](https://i.imgur.com/P4MpHZV.png)

The stick will only balance if its centre of mass is directly above some part of its support. Return `True` if the stick will balance and `False` if it will topple.

Both lists will be of equal length (that is, the stick and the terrain have equal width so that each index of the stick is directly above the corresponding index of the terrain). Every terrain will contain one, and only one, support.

## Examples:

![](https://i.imgur.com/PyMBsAl.png)

```
[2,3,2]
[0,1,0] ---> Perfectly balanced, return True

[5,1,1]
[0,1,0] ---> will topple to the left, return False

[3,3,4]
[0,1,0] ---> will topple to the right (but only just)

[7,1,1,1,1,1,1,1]
[0,1,1,0,0,0,0,0] ---> will balance, perfectly, without a doubt

[5, 3, 2, 8, 6]
[0, 0, 0, 1, 1] ---> will topple to the left

```

```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 = 'import math\n\ndef will_it_balance(stick, terrain):\n    numerator = 0\n    denominator = 0\n    for index, weight in enumerate(stick):\n        numerator += weight * (index+1)\n        denominator += weight\n    centerOfMass = numerator/denominator\n    centerOfMassLowCoord, centerOfMassHighCoord = math.floor(centerOfMass), math.ceil(centerOfMass)\n    return terrain[centerOfMassLowCoord-1]==1 and terrain[centerOfMassHighCoord-1]==1'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'will_it_balance'
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: 5574