There are some rabbits in Singapore Zoo. To feed them, Zookeeper bought $n$ carrots with lengths $a_1, a_2, a_3, \ldots, a_n$. However, rabbits are very fertile and multiply very quickly. Zookeeper now has $k$ rabbits and does not have enough carrots to feed all of them. To solve this problem, Zookeeper decided to cut the carrots into $k$ pieces. For some reason, all resulting carrot lengths must be positive integers.

Big carrots are very difficult for rabbits to handle and eat, so the time needed to eat a carrot of size $x$ is $x^2$.

Help Zookeeper split his carrots while minimizing the sum of time taken for rabbits to eat the carrots.


-----Input-----

The first line contains two integers $n$ and $k$ $(1 \leq n \leq k \leq 10^5)$: the initial number of carrots and the number of rabbits.

The next line contains $n$ integers $a_1, a_2, \ldots, a_n$ $(1 \leq a_i \leq 10^6)$: lengths of carrots.

It is guaranteed that the sum of $a_i$ is at least $k$.


-----Output-----

Output one integer: the minimum sum of time taken for rabbits to eat carrots.


-----Examples-----
Input
3 6
5 3 1

Output
15

Input
1 4
19

Output
91



-----Note-----

For the first test, the optimal sizes of carrots are $\{1,1,1,2,2,2\}$. The time taken is $1^2+1^2+1^2+2^2+2^2+2^2=15$

For the second test, the optimal sizes of carrots are $\{4,5,5,5\}$. The time taken is $4^2+5^2+5^2+5^2=91$.

```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 = 'import heapq\n\ndef sum_sqaure(a, k):\n    q, r = divmod(a, k)\n    return q**2 * (k-r) + (q+1)**2 * r\n\ndef diff(a, k):\n    return sum_sqaure(a, k+1) - sum_sqaure(a, k)\n\nn, k = map(int, input().split())\nnums = list(map(int, input().split()))\n\ncurr = sum(sum_sqaure(a, 1) for a in nums)\nQ = [(diff(a, 1), a, 1) for a in nums]\nheapq.heapify(Q)\nfor __ in range(k - n):\n    d, a, i = heapq.heappop(Q)\n    curr += d\n    heapq.heappush(Q, (diff(a, i+1), a, i+1))\nprint(curr)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13523