Magic The Gathering is a collectible card game that features wizards battling against each other with spells and creature summons. The game itself can be quite complicated to learn. In this series of katas, we'll be solving some of the situations that arise during gameplay. You won't need any prior knowledge of the game to solve these contrived problems, as I will provide you with enough information.

## Creatures

Each creature has a power and toughness. We will represent this in an array. [2, 3] means this creature has a power of 2 and a toughness of 3.

When two creatures square off, they each deal damage equal to their power to each other at the same time. If a creature takes on damage greater than or equal to their toughness, they die.

Examples:

- Creature 1 - [2, 3]
- Creature 2 - [3, 3]
- Creature 3 - [1, 4]
- Creature 4 - [4, 1]

If creature 1 battles creature 2, creature 1 dies, while 2 survives. If creature 3 battles creature 4, they both die, as 3 deals 1 damage to 4, but creature 4 only has a toughness of 1.

Write a function `battle(player1, player2)` that takes in 2 arrays of creatures. Each players' creatures battle each other in order (player1[0] battles the creature in player2[0]) and so on. If one list of creatures is longer than the other, those creatures are considered unblocked, and do not battle.

Your function should return an object (a hash in Ruby) with the keys player1 and player2 that contain the power and toughness of the surviving creatures.

Example:
```
Good luck with your battles!


Check out my other Magic The Gathering katas:


Magic The Gathering #1: Creatures
Magic The Gathering #2: Mana

```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 battle(player1, player2):\n  rem1=[c for i,c in enumerate(player1) if i>=len(player2) or c[1]>player2[i][0]]\n  rem2=[c for i,c in enumerate(player2) if i>=len(player1) or c[1]>player1[i][0]]\n  return {'player1':rem1, 'player2':rem2}"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'battle'
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: 5992