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.*;
import java.io.*;

public class _1428E {
    static int[] MODS = {1000000007, 998244353, 1000000009};
    static int MOD = MODS[0];

    public static void main(String[] args) {
        sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
        int n = sc.nextInt();
        int k = sc.nextInt();
        int[] arr = new int[n];
        scan(arr);
        PriorityQueue<Carrot> pq = new PriorityQueue<>();
        for (int i = 0; i < n; i++) {
            pq.add(new Carrot(arr[i], 1));
        }
        int pieces = n;
        while (pieces < k) {
            Carrot c = pq.poll();
            c.pieces++;
            pieces++;
            pq.add(c);
        }
        long time = 0;
        while (!pq.isEmpty()) {
            Carrot c = pq.poll();
            time += c.time(c.pieces);
        }
        out.println(time);
        out.close();
    }

    static class Carrot implements Comparable<Carrot> {
        int length;
        int pieces;
        Carrot(int l, int p) {
            length = l;
            pieces = p;
        }
        long time(int p) {
            int low = length / p;
            int num = length % p;
            return (long) (p - num) * low * low + (long) num * (low+1) * (low+1);
        }
        long inc() {
            return time(pieces) - time(pieces+1);
        }
        public int compareTo(Carrot other) {
            return Long.compare(other.inc(), inc());
        }
    }

    public static int[] sort(int[] arr) {
        ArrayList<Integer> list = new ArrayList<>();
        for (int i = 0; i < arr.length; i++) {
            list.add(arr[i]);
        }
        Collections.sort(list);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = list.get(i);
        }
        return arr;
    }

    public static void scan(int[] arr) {
        for (int i = 0; i < arr.length; i++) {
            arr[i] = sc.nextInt();
        }
    }

    public static MyScanner sc;
    public static PrintWriter out;

    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}
