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 heapq import heappush, heappop

def f(length, n_piece):
    width = length // n_piece
    extra = length - width * n_piece
    return width ** 2 * (n_piece - extra) + (width + 1) ** 2 * extra


def solve():
    N, K = map(int, input().split())
    A = [int(x) for x in input().split()]

    ans = sum(a ** 2 for a in A)
    heap = []
    for i, a in enumerate(A):
        decrease = f(a, 2) - f(a, 1)
        n_piece = 2
        heappush(heap, (decrease, a, n_piece))

    for _ in range(K - N):
        decrease, a, n_piece = heappop(heap)
        ans += decrease
        
        decrease = f(a, n_piece + 1) - f(a, n_piece)
        n_piece = n_piece + 1
        heappush(heap, (decrease, a, n_piece))

    return ans

print(solve())

# import matplotlib.pyplot as plt
# fig, ax = plt.subplots()
# xs = list(range(1, 30))
# ys = [f(25, x) for x in xs]
# ax.plot(xs, ys, '.-')
# ax.set_xlabel('#piece')
# ax.set_ylabel('f(25, x)')
# plt.show()
