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, stdout
from heapq import heappush, heappop

# 5 3 1, 6
# 2 3 3 1
# 2 2 1 3 1
# 2 2 1 2 1 1


# 10, 3 => 3, 3, 4
def calc(x, y):
    a = x // y
    l = x - y * a
    r = a * a * (y - l) + (a + 1) * (a + 1) * l
    return r


n, k = map(int, stdin.readline().split())
a_a = list(map(int, stdin.readline().split()))

res = 0
hpa = []
for i in range(n):
    res += a_a[i] * a_a[i]
    heappush(hpa, [calc(a_a[i], 2) - calc(a_a[i], 1), 2, i])

for i in range(k-n):
    m_a = heappop(hpa)
    res += m_a[0]

    heappush(hpa, [calc(a_a[m_a[2]], m_a[1] + 1) - calc(a_a[m_a[2]], m_a[1]), m_a[1] + 1, m_a[2]])

stdout.write(str(res))
