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 java.util.PriorityQueue;
import java.util.Scanner;

public class Program {
    static class Carrot {
        long splitCost;
        int length;
        int parts;

        public Carrot(long splitCost, int length, int parts) {
            this.splitCost = splitCost;
            this.length = length;
            this.parts = parts;
        }
    }

    private static long square(int x) {
        return (long) x * x;
    }

    private static long cost(int length, int parts) {
        int units = length / parts;
        int extra = length - units * parts;
        return (parts - extra) * square(units) + extra * square(units + 1);
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        int[] a = new int[n];
        long sum = 0;
        PriorityQueue<Carrot> priorityQueue = new PriorityQueue<>((o1, o2) -> {
            if(o1.splitCost<o2.splitCost) return 1;
            else if(o1.splitCost==o2.splitCost)
            {
                if(o1.length<o2.length) return 1;
                else if(o1.length==o2.length) return o1.parts<=o2.parts?1:-1;
                else return -1;
            }
            else return -1;
        });
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
            sum += square(a[i]);
            priorityQueue.add(new Carrot(cost(a[i], 1) - cost(a[i], 2), a[i], 2));
        }
        for (int i = 0; i < k - n; i++) {
            Carrot carrot = priorityQueue.remove();
            sum -= carrot.splitCost;
            priorityQueue.add(new Carrot(cost(carrot.length, carrot.parts) - cost(carrot.length, carrot.parts + 1), carrot.length, carrot.parts + 1));
        }
        System.out.println(sum);
    }
}
