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
from heapq import heappush as push, heappop as pop, heapify

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

q = [int(x) for x in stdin.readline().split()]

def f(l,p):
    base = l//p
    leftover = l-base*p
    return (p-leftover)*base*base+ leftover*(base+1)*(base+1)

carrots = []
for carrot in q:
    push(carrots, ( -(f(carrot,1)-f(carrot,2)), carrot, 1))

for _ in range(k-n):
    tmp = pop(carrots)
    carrot = tmp[1]
    cuts = tmp[2] +1
    push(carrots, ( -(f(carrot,cuts)-f(carrot,cuts+1)), carrot, cuts))

print(sum(f(y,z) for x,y,z in carrots))
