In the wake of the npm's `left-pad` debacle, you decide to write a new super padding method that superceds the functionality of `left-pad`. Your version will provide the same functionality, but will additionally add right, and justified padding of string -- the `super_pad`.

Your function `super_pad` should take three arguments: the string `string`, the width of the final string `width`, and a fill character `fill`. However, the fill character can be enriched with a format string resulting in different padding strategies. If `fill` begins with `'<'` the string is padded on the left with the remaining fill string and if `fill` begins with `'>'` the string is padded on the right. Finally, if `fill` begins with `'^'` the string is padded on the left and the right, where the left padding is always greater or equal to the right padding. The `fill` string can contain more than a single char, of course. 

Some examples to clarify the inner workings:

- `super_pad("test", 10)` returns "      test"
- `super_pad("test", 10, "x")` returns `"xxxxxxtest"`
- `super_pad("test", 10, "xO")` returns `"xOxOxOtest"`
- `super_pad("test", 10, "xO-")` returns `"xO-xO-test"`
- `super_pad("some other test", 10, "nope")` returns `"other test"`
- `super_pad("some other test", 10, "> ")` returns `"some other"`
- `super_pad("test", 7, ">nope")` returns `"testnop"`
- `super_pad("test", 7, "^more complex")` returns `"motestm"`
- `super_pad("test", 7, "")` returns `"test"`

The `super_pad` method always returns a string of length `width` if possible. We expect the `width` to be positive (including 0) and the fill could be also an empty string.

```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 = 'def super_pad(string, width, fill=" "):\n    str_len = len(string)\n    ###### RIGHT\n    if fill.find(\'>\')+1:\n        fill = fill[1:]\n        fill_len = len(fill)\n        to_fill_len = width - str_len\n        if width < str_len: # For any: fill_len\n            retval = string[0:width]\n        # For all below: width >= str_len\n        elif fill_len == 0:\n            retval = string\n        elif fill_len == 1:\n            RHS_to_fill = width - str_len\n            retval = string + fill*RHS_to_fill\n        elif fill_len > 1:\n            chunks = int(to_fill_len / fill_len)\n            parts  = to_fill_len % fill_len\n            total_len = (chunks*fill_len+parts) # DEBUG\n            retvalb = string + (fill*(chunks+1))[0:total_len]\n            retval = retvalb\n        else:\n            retval = \'RIGHT: Oops\'\n    ##### CENTER\n    elif fill.find(\'^\')+1:\n        fill = fill[1:]\n        fill_len = len(fill)\n        to_fill_len = int((width - str_len) / 2)\n        LHS_to_fill_len = to_fill_len + (width - str_len) % 2\n        RHS_to_fill_len = to_fill_len\n        if width < str_len: # For any: fill_len\n            retval = string[0:width]\n        # For all below: width >= str_len\n        elif fill_len == 0:\n            retval = string\n        else:\n            LHS_chunks = int(LHS_to_fill_len / fill_len)\n            LHS_parts  = LHS_to_fill_len % fill_len\n            LHS_total_len = (LHS_chunks*fill_len+LHS_parts)\n            RHS_chunks = int(RHS_to_fill_len / fill_len)\n            RHS_parts  = RHS_to_fill_len % fill_len\n            RHS_total_len = (RHS_chunks*fill_len+RHS_parts)\n            retval = (fill*(LHS_chunks+1))[0:LHS_total_len] + string + (fill*(RHS_chunks+1))[0:RHS_total_len]\n    ###### LEFT\n    else:\n        if fill.find(\'<\')+1:fill = fill[1:]\n        fill_len = len(fill)\n        if width < str_len: # For any: fill_len\n            retval = string[str_len-width:]\n        # For all below: width >= str_len\n        elif fill_len == 0:\n            retval = string\n        elif fill_len == 1:\n            LHS_to_fill = width - str_len\n            retval = fill*LHS_to_fill + string\n        elif fill_len  > 1:\n            LHS_to_fill = width - str_len\n            fill_count = int(LHS_to_fill / fill_len)\n            fill_count_rem = LHS_to_fill % fill_len\n            retval = fill*fill_count + fill[0:fill_count_rem] +string\n        else:\n            retval = \'Left_TEST_Left\'\n    return retval\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'super_pad'
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: 6415