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 math import inf
from heapq import heapify, heappush, heappop


def make_heap_item(a, new_pieces_n):
    weight = take_min_final_sum(a, new_pieces_n-1) - take_min_final_sum(a, new_pieces_n)
    return (-weight, a, new_pieces_n)


def take_min_final_sum(a, pieces_n):
    if a < pieces_n:
        return +inf
    lower_term, higher_term_n = divmod(a, pieces_n)
    higher_term = lower_term + 1
    lower_term_n = pieces_n - higher_term_n
    return lower_term**2 * lower_term_n + higher_term**2 * higher_term_n


def read_ints():
    return map(int, input().split())


n, k = read_ints()
a_seq = tuple(read_ints())

best_new_maxs = [make_heap_item(a, 2) for a in a_seq]
heapify(best_new_maxs)

for i in range(k - n):
    neg_best_new_max, initial_value, pieces_n = heappop(best_new_maxs)
    pieces_n += 1
    new_item = make_heap_item(initial_value, pieces_n)
    heappush(best_new_maxs, new_item)


result = sum(
    take_min_final_sum(a, pieces_n_plus_1-1)
    for _, a, pieces_n_plus_1 in best_new_maxs
)

print(result)
