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 heapq

def calc(l,n):
    div=l//n
    mod=l%n
    #returns the minimum time required to consume a carrot of inititl
    #length l when cut into n pieces
    return(div*div*n+(2*div+1)*mod)

n,k=map(int,input().split())
a=[int(i) for i in input().split()]
cur=[1]*(n)
heap=[]
for i in range(n):
    v=a[i]
    #heap stores the indexof the carrot which when cut will give the
    #maximum reduction in time
    heapq.heappush(heap,(calc(v,2)-calc(v,1),i))
ans=0
for i in range(k-n):
    _,best=heapq.heappop(heap)
    cur[best]+=1
    cuts=cur[best]
    heapq.heappush(heap,(calc(a[best],cuts+1)-calc(a[best],cuts),best))
for i in range(n):
    ans+=calc(a[i],cur[i])
#print(cur)
print(ans)
    

                
                
            
            



                       
                               
        
    
