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 sys
readline = sys.stdin.readline
from heapq import heappop as hpp, heappush as hp


INF = 10**9+7
def calc(A, x):
    if A < x:
        return INF
    d, r = divmod(A, x)
    return d*d*x+(2*d+1)*r

N, K = map(int, readline().split())
A = list(map(int, readline().split()))
Q = [(-calc(a, 1)+calc(a, 2), a, 1) for a in A]
Q.sort()
for _ in range(K-N):
    dif, a, x = hpp(Q)
    hp(Q, (-calc(a, x+1) + calc(a, x+2), a, x+1))

ans = 0
for _, a, x in Q:
    ans += calc(a, x)
print(ans)    
