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.
import math
import heapq


def score_with(size, cuts):
    if cuts == 0:
        return size**2
    sup = math.ceil(size/cuts)
    inf = sup-1
    mod = size % cuts
    if mod == 0:
        nbsup = cuts
        nbinf = 0
    else:
        nbsup = mod
        nbinf = cuts - mod
    # print('score with', size, cuts, ':', (sup**2) * nbsup + (inf**2) * nbinf)
    return (sup**2) * nbsup + (inf**2) * nbinf


def compute_savings(size, nb_cuts):
    return score_with(size, nb_cuts) - score_with(size, nb_cuts+1)


N, K = [int(_) for _ in input().split()]
A = [int(_) for _ in input().split()]
pq = []
score = 0

for el in A:
    score += el**2
    savings = compute_savings(el, 1)
    # print('push', el, savings)
    heapq.heappush(pq, (-savings, el, 1))

# print('initial score', score)

for i in range(K-N):
    neg_savings, sz, nb_cuts = heapq.heappop(pq)
    savings = -neg_savings
    # print('save', savings, 'by cutting', sz)
    score -= savings
    next_savings = compute_savings(sz, nb_cuts+1)
    heapq.heappush(pq, (-next_savings, sz, nb_cuts+1))

print(score)
