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.Arrays;
import java.util.PriorityQueue;
import java.util.AbstractQueue;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.Comparator;
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;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskE solver = new TaskE();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskE {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int N = in.nextInt();
            int K = in.nextInt() - N;
            long[] cost = new long[N];
            long[] tot = new long[N];
            Arrays.fill(tot, 1);
            long[] a = new long[N];
            long[] chg = new long[N];
            for (int i = 0; i < N; i++) {
                a[i] = in.nextInt();
                cost[i] = a[i] * a[i];
                chg[i] = getSplit(a[i], ++tot[i]) - cost[i];
            }
            PriorityQueue<Integer> queue = new PriorityQueue<>(new Comparator<Integer>() {

                public int compare(Integer integer, Integer t1) {
                    return Long.compare(chg[integer], chg[t1]);
                }
            });
            for (int i = 0; i < N; i++) {
                queue.add(i);
            }
            while (K-- > 0) {
                int next = queue.remove();
                cost[next] += chg[next];
                chg[next] = getSplit(a[next], ++tot[next]) - cost[next];
                queue.add(next);
            }
            long ans = 0;
            for (int i = 0; i < N; i++) {
                ans += cost[i];
            }
            out.println(ans);
        }

        long getSplit(long S, long P) {
            long mid = S / P;
            return mid * mid * (P - (S - mid * P)) + (S - mid * P) * (mid + 1) * (mid + 1);
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

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

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

    }
}

