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
N, K = map(int, input().split())
X = list(map(int, input().split()))
Y = [((x//2)**2 + (x//2+x%2)**2 - x**2, x**2, 1, x) for x in X]
l = []
for x in Y:
    heapq.heappush(l, x)
#print(l)
R = 0
for _ in range(K-N):
    t, x, y, s = heapq.heappop(l)
    nx = x+t
    y += 1
    k, m = divmod(s, y+1)
#    print(k,m,nx)
    nt = (y+1-m)*(k**2) + m*((k+1)**2) - nx
#    print(nt)
    heapq.heappush(l, (nt, nx, y, s))
#    print(l)
    
R = 0
for t, x, y, s in l:
    R += x
print(R)
