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.
mod = 1000000007
eps = 10**-9


def main():
    import sys
    from heapq import heappop, heappush
    input = sys.stdin.readline

    def calc(a, d):
        return ((a // d + 1) ** 2) * (a % d) + ((a // d) ** 2) * (d - a%d)

    N, K = map(int, input().split())
    A = list(map(int, input().split()))

    ans = 0
    pq = []
    for a in A:
        ans += a * a
        if a > 1:
            heappush(pq, (calc(a, 2) - calc(a, 1), a, 2))

    for _ in range(K - N):
        g, a, d = heappop(pq)
        ans += g
        if a > d:
            heappush(pq, (calc(a, d+1) - calc(a, d), a, d+1))
    print(ans)


if __name__ == '__main__':
    main()
