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 *
Z=lambda:map(int,input().split())
V=lambda n,k:(n%k)*(n//k+1)**2+(k-n%k)*(n//k)**2
D=lambda n,k:V(n,k)-V(n,k+1)
n,k=Z();w=k-n+1;N=n*w;a=[*Z()];s=sum(i*i for i in a);d=0
b=[-D(a[i],1)*N-i for i in range(n)];heapify(b)
for i in range(w-1):
 v=-heappop(b);d+=v//N;i=v%n;l=(v//n)%w
 heappush(b,-D(a[i],l+2)*N-(l+1)*n-i)
print(s-d)