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    if fill == \'\':\n        return string\n    if width == 0:\n        return \'\'\n    diff = width-len(string)\n    if diff <= 0:\n        if fill[0] == \'>\':\n            return string[:width]\n        elif fill[0] == \'^\':\n            a = abs(diff)//2\n            b = abs(diff)-a\n            if a == 0 and diff == -1:\n                return string[:-1]\n            return string[b:] + string[:-a]\n        elif fill[0] == \'<\':\n            fill = fill[1:]\n        return string[-width:]\n    else:\n        if fill[0] == \'>\':\n            fill = fill[1:]\n            if len(fill) > diff:\n                return string + fill[:diff]\n            else:\n                ans, i = \'\', 0\n                while i < diff:\n                    ans += fill\n                    if len(ans) >= diff:\n                        ans = ans[:diff]\n                        break\n                    i += 1\n                return string + ans        \n        elif fill[0] == \'^\':\n            fill = fill[1:]\n            a = diff//2\n            b = diff-a\n            if len(fill) > diff:\n                return fill[:b] + string + fill[:a]\n            else:\n                ans1, i, ans2 = \'\', 0, \'\'\n                while i < b:\n                    ans1 += fill\n                    ans2 += fill\n                    if len(ans2) >= diff//2 :\n                        ans1 = ans1[:a]\n                        if len(ans1) >= diff-len(ans2):\n                            ans2 = ans2[:b]\n                            break\n                    i += 1\n                return ans2 + string + ans1\n        elif fill[0] == \'<\':\n            fill = fill[1:]\n            if len(fill) > diff:\n                return fill[:diff] + string\n            else:\n                ans, i = \'\', 0\n                while i < diff:\n                    ans += fill\n                    if len(ans) >= diff:\n                        ans = ans[:diff]\n                        break\n                    i += 1\n                return ans + string\n        else:\n            if len(fill) > diff:\n                return fill[:diff] + string\n            else:\n                ans, i = \'\', 0\n                while i < diff:\n                    ans += fill\n                    if len(ans) >= diff:\n                        ans = ans[:diff]\n                        break\n                    i += 1\n                return ans + string'
_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: 6735