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 *
n, k = map(int, input().split())
a = list(map(int, input().split()))

count = [0]*n
b = []

for i in range(n):
    x = a[i]
    diff = x**2 - ((x//2)**2+((x+1)//2)**2)
    b.append((-diff, i))

heapify(b)

for _ in range(k-n):
    diff, index = heappop(b)
    diff *= -1
    c = count[index] + 1
    count[index] = c
    num = a[index]
    c += 1

    now = 0
    rem = num % c
    length = num // c

    now += length**2 * (c-rem)
    now += (length+1)**2 * (rem)

    c += 1
    next = 0
    rem = num % c
    length = num // c
    next += length**2 * (c-rem)
    next += (length+1)**2 * (rem)

    heappush(b, (-abs(now-next), index))

ans = 0
for i in range(n):
    c = count[i]+1
    num = a[i]

    rem = num % c
    length = num // c
    ans += length**2 * (c-rem)
    ans += (length+1)**2 * (rem)

print(ans)
