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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

public class Task5 {

    public static void main(String[] args) throws IOException {
        new Task5().solve();
    }

    private void solve() throws IOException {
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);

        StringTokenizer tokenizer = new StringTokenizer(f.readLine());
        int n = Integer.parseInt(tokenizer.nextToken());
        int k = Integer.parseInt(tokenizer.nextToken());
        tokenizer = new StringTokenizer(f.readLine());
        PriorityQueue<Carrot> carrots = new PriorityQueue<Carrot>();
        for (int i = 0; i < n; i++) {
            carrots.add(new Carrot(Integer.parseInt(tokenizer.nextToken()), 1));
        }

        while (n < k) {
            Carrot carrot = carrots.remove();
            carrots.add(new Carrot(carrot.length, carrot.parts +1));
            n++;
        }

        long sum = 0;
        for (Carrot carrot : carrots) sum += valueOfCut(carrot.length, carrot.parts);
        out.println(sum);
        out.close();
    }


    private static class Carrot implements Comparable<Carrot> {
        int length;
        int parts;

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

        @Override
        public int compareTo(Carrot o) {
            return Long.compare(this.additionalCutValue(), o.additionalCutValue());
        }

        private long additionalCutValue() {
            return valueOfCut(this.length, this.parts + 1) - valueOfCut(this.length, this.parts);
        }
    }

    private static long valueOfCut(int length, int parts) {
        long newLength = length / parts;
        int longerParts = length % parts;
        long newValue = (long) (longerParts) * (newLength + 1) * (newLength + 1) + (long) (parts - longerParts) * newLength * newLength;
        return newValue;
    }
}
