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 implements Comparable<Carrot> {
        int length;
        int parts;

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

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

        private long cost() {
            int biggerSize = length % parts;
            int smallerSize = parts - biggerSize;
            long smallerCost = square(length / parts);
            long biggerCost = square(length / parts + 1);
            return smallerSize * smallerCost + biggerSize * biggerCost;
        }

        private long decreaseInCost() {
            long originalCost = cost();
            parts++;
            long newCost = cost();
            parts--;
            return originalCost - newCost;
        }

        @Override
        public int compareTo(Carrot carrot) {
            return Long.compare(carrot.decreaseInCost(), decreaseInCost());
        }
    }

    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<>();
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
            priorityQueue.add(new Carrot(a[i], 1));
        }
        for (int i = 0; i < k - n; i++) {
            Carrot carrot = priorityQueue.remove();
            carrot.parts++;
            priorityQueue.add(carrot);
        }
        while (!priorityQueue.isEmpty()) {
            sum += priorityQueue.remove().cost();
        }
        System.out.println(sum);
    }
}
