There are some rabbits in Singapore Zoo. To feed them, Zookeeper bought n carrots with lengths a_1, a_2, a_3, …, 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 ≤ n ≤ k ≤ 10^5): the initial number of carrots and the number of rabbits.

The next line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 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.
from sys import stdin

input = stdin.readline
from heapq import heappush, heappop


def solve():
    n, k = map(int, input().split())
    a = list(map(int, input().split()))
    if n == k:
        print(sum(i**2 for i in a))
        return
    def cal(l, pieces):
        optimal, extra = divmod(l, pieces)
        return (pieces - extra) * optimal ** 2 + extra * (optimal + 1) ** 2

    h = []
    for i in a:
        heappush(h, [cal(i, 2) - cal(i, 1), i, 2])
    res = sum(i**2 for i in a)
    while n < k:
        n += 1
        d,l,p = heappop(h)
        res += d
        heappush(h,[cal(l,p+1) - cal(l,p),l,p+1])
    print(res)


if __name__ == '__main__':
    # t = int(input())
    # for _ in range(t):
    solve()
