## Task

You are given three non negative integers `a`, `b` and `n`, and making an infinite sequence just like fibonacci sequence, use the following rules:

- step 1: use `ab` as the initial sequence.
- step 2: calculate the sum of the last two digits of the sequence, and append it to the end of sequence.
- repeat step 2 until you have enough digits

Your task is to complete the function which returns the `n`th digit (0-based) of the sequence.

### Notes:

- `0 <= a, b <= 9`, `0 <= n <= 10^10`
- `16` fixed testcases
- `100` random testcases, testing for correctness of solution
- `100` random testcases, testing for performance of code
- All inputs are valid.
- Pay attention to code performance.


## Examples

For `a = 7, b = 8 and n = 9` the output should be `5`, because the sequence is:
```
78 -> 7815 -> 78156 -> 7815611 -> 78156112 -> 781561123 -> 7815611235 -> ...
``` 

and the 9th digit of the sequence is `5`.

---

For `a = 0, b = 0 and n = 100000000` the output should be `0`, because all the digits in this sequence are `0`.

```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 = "# Precompute all 2 digit suffixes into an associated prefix and repeating loop\n# E.g. build until we get two repeating values:\n#   98 -> [17, 8, 15, 6, 11, 2, 3, 5, 8, 13, 4, 7, 11, 2] (Note: [11, 2] is repeated)\n#   -> Prefix '17815611', Loop: '2358134711'\n#\n# Now any number ending with 98 has a predefined prefix and cycle, e.g.:\n#   123 + 598 -> 123598 -> 98 -> Prefix '17815611', Loop: '2358134711'\n# Hence 123 + 598 starts with '12359817815611' and then repeats '2358134711' indefinitely\n\n# Dict[str, Tuple[str, str]]\nlookup = {}\nfor i in range(10):\n    for j in range(10):\n        start = f'{i}{j}'\n        n = int(start)\n        s = [0, n]\n        seen = {}\n        while True:\n            x = s[-1]\n            if x < 10:\n                x = x + s[-2] % 10\n            else:\n                x = (x // 10) + (x % 10)\n            \n            pair = (s[-1], x)\n            if pair not in seen:\n                s.append(x)\n                seen[pair] = len(s)\n            else:\n                # idx is the point where prefix finishes and loop starts\n                idx = seen[pair] - 1\n                prefix = s[2:idx]  # Skip the leading zero and the starting value\n                loop = s[idx:]\n                lookup[start] = (''.join(map(str, prefix)), ''.join(map(str, loop)))\n                break\n\ndef find(a, b, n):\n    start = f'{a}{b}'[-2:].rjust(2, '0')\n    prefix, loop = lookup[start]\n    s = str(a) + str(b) + prefix + loop\n    \n    if n < len(s):\n        # Digit in initial supplied digits, the sum of their last two digits or the prefix\n        return int(s[n])\n\n    # Digit is in the loop\n    m = (n - len(s)) % len(loop)\n    return int(loop[m])\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'find'
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: 5690