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, gettrace
from heapq import heappush, heappop

if gettrace():
    inputi = input
else:
    def input():
        return next(stdin)[:-1]


    def inputi():
        return stdin.buffer.readline()

def cost(ln, pieces):
    extras = ln%pieces
    return ((ln//pieces) * (ln//pieces)) * pieces + 2*(ln//pieces)*extras + extras

def cost_decrease(ln, pieces):
    return cost(ln, pieces) - cost(ln, pieces+1)

def main():
    n,k = map(int, inputi().split())
    aa = [int(a) for a in inputi().split()]
    hp = []
    for a in aa:
        heappush(hp, (-cost_decrease(a, 1), a, 1))
    for _ in range(n,k):
        _, a, c = heappop(hp)
        heappush(hp, (-cost_decrease(a, c+1), a, c+1))
    print(sum(cost(a, c) for _,a,c in hp))







if __name__ == "__main__":
    main()
