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 sys
from heapq import heapify, heapreplace

n, k, *aaa = map(int, sys.stdin.buffer.read().split())

ans = 0
for a in aaa:
    ans += a * a

hq = []
for a in aaa:
    p = 1
    d, m = divmod(a, p + 1)
    cost = d * d * (p + 1 - m) + (d + 1) * (d + 1) * m
    hq.append((cost - a * a, a * a, a, p))

heapify(hq)

for _ in range(k - n):
    dec, cur, a, p = hq[0]
    ans += dec
    cur += dec
    p += 1
    d, m = divmod(a, p + 1)
    cost = d * d * (p + 1 - m) + (d + 1) * (d + 1) * m
    heapreplace(hq, (cost - cur, cur, a, p))

print(ans)
