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

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskE1 solver = new TaskE1();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskE1 {
        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            int n = in.nextInt();
            int k = in.nextInt();
            int[] a = new int[n];
            PriorityQueue<Item> pq = new PriorityQueue<>();
            long ans = 0;
            int[] parts = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = in.nextInt();
                ++parts[i];
                ans += f(a[i], parts[i]);
                if (parts[i] < a[i]) {
                    pq.offer(new Item(i, f(a[i], parts[i] + 1) - f(a[i], parts[i])));
                }
            }
            for (int step = 0; step < k - n; step++) {
                Item it = pq.poll();
                ans += it.val;
                int i = it.id;
                ++parts[i];
                if (parts[i] < a[i]) {
                    pq.offer(new Item(i, f(a[i], parts[i] + 1) - f(a[i], parts[i])));
                }
            }
            out.println(ans);
        }

        private long f(int x, int parts) {
            long small = x / parts;
            long large = small + 1;
            long numLarge = x % parts;
            long numSmall = parts - numLarge;
            long cost = small * small * numSmall + large * large * numLarge;
            return cost;
        }

        class Item implements Comparable<Item> {
            int id;
            long val;

            public Item(int id, long val) {
                this.id = id;
                this.val = val;
            }

            public int compareTo(Item o) {
                return Long.compare(val, o.val);
            }

        }

    }

    static class FastScanner {
        private BufferedReader in;
        private StringTokenizer st;

        public FastScanner(InputStream stream) {
            in = new BufferedReader(new InputStreamReader(stream));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(in.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

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

    }
}

