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

import heapq

def cut(i, k):
	t = (i + k - 1) // k
	amt = i % k
	if amt == 0:
		amt = k
	#print(f"want to cut {i} into {k} pieces, retarget to {t}, have {amt} of {t} and {k-amt} of {t-1}")
	return amt * t **2 + (k - amt) * (t-1)**2

h = []
for x in a:
	heapq.heappush(h, (cut(x,2)-cut(x, 1), x, 1))

for _ in range(k - len(a)):
	_,y,z = heapq.heappop(h)
	heapq.heappush(h, (cut(y,z+2)-cut(y, z+1), y, z+1))

#print("DONE")
print(sum(cut(y,z) for x,y,z in h))
