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 value(l,parts):
    len1 = l//parts
    len2 = len1+1 
    cnt2 = l%parts
    cnt1 = parts-cnt2 
    return cnt1*len1*len1 + cnt2*len2*len2
    

def solve(n,k,a):
    total = 0
    pq = []
    for i in range(n):
        total += a[i]*a[i]
        heapq.heappush(pq,(-1*value(a[i],1)+value(a[i],2),a[i],2))
    for i in range(k-n):
        temp = heapq.heappop(pq)
        total += temp[0]
        a,b = temp[1],temp[2]
        heapq.heappush(pq,(-value(a,b)+value(a,b+1),a,b+1))
    return total
n,k = map(int,input().split())
a = list(map(int,input().split()))
print(solve(n,k,a))