# Story&Task
 The capital of Berland has n multifloor buildings. The architect who built up the capital was very creative, so all houses in the city were built in one row.

 Let's enumerate all the houses from left to right, starting with 0. A house is considered to be luxurious if the number of floors in it is strictly greater than in each house with larger number. In other words, a house is luxurious if the number of floors in it is strictly greater than in all houses, located to the right from it.

 The new architect is interested in n questions, the ith of them is the following: "how many floors should be added to the ith house to make it luxurious?" (For each i from 1 to n, inclusive). You need to help him cope with this task.

 Note that all these questions are independent from each other — the answer to the question for house i does not affect other answers (i.e., the floors to the houses are not actually added).

# Input/Output


 - `[input]` integer array `houses`

  Array of positive integers, representing the number of floors in each house.

  The ith element is the number of houses in the ith house.

  `1 ≤ houses.length ≤ 1000`


 - `[output]` an integer array

  An array has the same length as input array, the ith element represents the number of floors that should be added to the ith house to make it luxurious.
  
# Example

 For `houses = [1,2,3,1,2]`, the output should be `[3,2,0,2,0]`.
 ```
 For houses[0], 3 floors should be added, 
 then its floors is strictly greater than all houses of right side.
 
 For houses[1], 2 floors should be added.
 
 For houses[2], no need to add floor
 because it's already the luxurious.
 
 For houses[3], 2 floors need to added
 
 For houses[4], no house on the right, 
 so no need to add any floor.
 ```

```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 = 'from itertools import accumulate\n\ndef luxhouse(houses):\n    return [max(0, y-x+1) for x,y in zip(houses[::-1], accumulate([0] + houses[:0:-1], max))][::-1]'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'luxhouse'
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: 5966