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 heapq


def f(x, c):
    # time to eat a carrot of length cut into c pieces
    return (x % c) * (x // c + 1) ** 2 + (c - x % c) * (x // c) ** 2


def g(x, c):
    # c >= 2; marginal time saving after being cut into c-pieces
    return f(x, c) - f(x, c - 1)


n, k = [int(x) for x in input().split(' ')]
a = [int(x) for x in input().split(' ')]
b = [(g(x, 2), 1, x) for x in a]

heapq.heapify(b)

for i in range(k - n):
    y = heapq.heappop(b)
    y = (g(y[2], y[1] + 2), y[1] + 1, y[2])
    heapq.heappush(b, y)

c = 0
for z in b:
    c += f(z[2], z[1])
print(c)

