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(" "))


def val(l,nums):
    unit=l//nums
    extra=l-unit*nums
    return (nums-extra)*unit*unit+extra*(unit+1)*(unit+1)
    
pq=[]
arr=list(map(int,input().split(" ")))

total=0
for x in range(n):
    total+=arr[x]*arr[x]
    heappush(pq,(-val(arr[x],1)+val(arr[x],2),arr[x],2))

for x in range(k-n):
    temp=heappop(pq)
    total+=temp[0]
    a,b=temp[1],temp[2]
    heappush(pq,(-val(a,b)+val(a,b+1),a,b+1))

print(total)