John has some amount of money of which he wants to deposit a part `f0` to the bank at the beginning
of year `1`. He wants to withdraw each year for his living an amount `c0`.

Here is his banker plan:

- deposit `f0` at beginning of year 1
- his bank account has an interest rate of `p` percent per year, constant over the years
- John can withdraw each year `c0`, taking it whenever he wants in the year; he must take account of an inflation of `i` percent per year in order to keep his quality of living. `i` is supposed to stay constant over the years.
- all amounts f0..fn-1, c0..cn-1 are truncated by the bank to their integral part
- Given f0, `p`, c0, `i` 
the banker guarantees that John will be able to go on that way until the `nth` year.

# Example:

```
f0 = 100000, p = 1 percent, c0 = 2000, n = 15, i = 1 percent
```

```
beginning of year 2 -> f1 = 100000 + 0.01*100000 - 2000 = 99000;  c1 = c0 + c0*0.01 = 2020 (with inflation of previous year)
```

```
beginning of year 3 -> f2 =  99000 + 0.01*99000 - 2020  = 97970;  c2 = c1 + c1*0.01 = 2040.20 
(with inflation of previous year, truncated to 2040)
```

```
beginning of year 4 -> f3 =  97970 + 0.01*97970 - 2040  = 96909.7 (truncated to 96909); 
c3 = c2 + c2*0.01 = 2060.4 (with inflation of previous year, truncated to 2060)
```
and so on...

John wants to know if the banker's plan is right or wrong.
Given parameters `f0, p, c0, n, i` build a function `fortune` which returns `true` if John can make a living until the `nth` year
and `false` if it is not possible.

# Some cases:
```
fortune(100000, 1, 2000, 15, 1) -> True
fortune(100000, 1, 10000, 10, 1) -> True
fortune(100000, 1, 9185, 12, 1) -> False

For the last case you can find below the amounts of his account at the beginning of each year:
100000, 91815, 83457, 74923, 66211, 57318, 48241, 38977, 29523, 19877, 10035, -5
```
f11 = -5 so he has no way to withdraw something for his living in year 12.

> **Note:** Don't forget to convert the percent parameters as percentages in the body of your function: if a parameter percent is 2 you have to convert it to 0.02.

```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 fortune(f0, p, c0, n, i):\n    f0 = math.trunc(f0 * (1 + p / 100) - c0)\n    c0 = c0 * (1 + i/100)\n    if n == 2:\n        return True if f0 >= 0 else False\n    else:\n        return fortune(f0, p, c0, n-1, i)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'fortune'
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: 8728