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
input = sys.stdin.buffer.readline
from heapq import heappush, heappop

def min_val(amt, parts):
    base = amt//parts
    extra = amt % parts
    return extra*(base + 1)**2 + (parts-extra)*(base)**2

def prog():
    n,k = map(int,input().split())
    a = list(map(int,input().split()))

    heap = []
    total_time = 0
    for length in a:
        total_time += length**2
        heappush(heap, [min_val(length, 2) - length**2, [length,2]])

    for i in range(k-n):
        curr = heappop(heap)
        total_time += curr[0]
        heappush(heap, [min_val(curr[1][0], curr[1][1] + 1) - min_val(curr[1][0],curr[1][1]), [curr[1][0],curr[1][1] +1]])
        
    print(total_time)
    
prog()
