We all know the impressive story of Robin Hood. Robin Hood uses his archery skills and his wits to steal the money from rich, and return it to the poor.

There are n citizens in Kekoland, each person has c_{i} coins. Each day, Robin Hood will take exactly 1 coin from the richest person in the city and he will give it to the poorest person (poorest person right after taking richest's 1 coin). In case the choice is not unique, he will select one among them at random. Sadly, Robin Hood is old and want to retire in k days. He decided to spend these last days with helping poor people. 

After taking his money are taken by Robin Hood richest person may become poorest person as well, and it might even happen that Robin Hood will give his money back. For example if all people have same number of coins, then next day they will have same number of coins too. 

Your task is to find the difference between richest and poorest persons wealth after k days. Note that the choosing at random among richest and poorest doesn't affect the answer.


-----Input-----

The first line of the input contains two integers n and k (1 ≤ n ≤ 500 000, 0 ≤ k ≤ 10^9) — the number of citizens in Kekoland and the number of days left till Robin Hood's retirement.

The second line contains n integers, the i-th of them is c_{i} (1 ≤ c_{i} ≤ 10^9) — initial wealth of the i-th person.


-----Output-----

Print a single line containing the difference between richest and poorest peoples wealth.


-----Examples-----
Input
4 1
1 1 4 2

Output
2

Input
3 1
2 2 2

Output
0



-----Note-----

Lets look at how wealth changes through day in the first sample.  [1, 1, 4, 2]  [2, 1, 3, 2] or [1, 2, 3, 2] 

So the answer is 3 - 1 = 2

In second sample wealth will remain the same for each person.

```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

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'n, k = map(int, input().split())\nnums = list(map(int, input().split()))\ntotal = sum(nums)\navg = int(total / n)\n\ndef check1(nums, target, K):\n    for x in nums:\n        if K < 0:\n            return False\n        if x < target:\n            K -= target - x\n    return K >= 0\n\ndef check2(nums, target, K):\n    for x in nums:\n        if K < 0:\n            return False\n        if x > target:\n            K -= x - target\n    return K >= 0\n\nl1, r1 = min(nums), avg + 1\nwhile l1 + 1 < r1:\n    mid = (l1 + r1) >> 1\n    if check1(nums, mid, k):\n        l1 = mid\n    else:\n        r1 = mid\n\nif check2(nums, avg + (0 if total % n == 0 else 1), k):\n    r2 = avg + (0 if total % n == 0 else 1)\nelse:\n    l2, r2 = avg + (0 if total % n == 0 else 1), max(nums)\n    while l2 + 1 < r2:\n        mid = (l2 + r2) >> 1\n        if check2(nums, mid, k):\n            r2 = mid\n        else:\n            l2 = mid\n\nprint(r2 - l1)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13351