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.*;
import java.math.BigInteger;
import java.util.*;


public class E {

  void solve() throws IOException {
    int n = nextInt();
    int k = nextInt();
    PriorityQueue<Group> queue = new PriorityQueue<>();
    for (int i = 0; i < n; i++) {
      queue.add(new Group(nextInt()));
    }
    while (n < k) {
      Group g = queue.poll();
      g.addCut();
      queue.add(g);
      n++;
    }
    long ans = queue.stream().mapToLong(Group::calcScore).sum();
    out.println(ans);
  }

  class Group implements Comparable<Group> {
    int len;
    int cut;
    long improve;

    public Group(int len) {
      this.len = len;
      this.cut = 1;
      if (len == 1) {
        improve = 0;
      } else {
        improve = calcScore(1) - calcScore(2);
      }
    }

    public void addCut() {
      cut++;
      if (len == cut) {
        improve = 0;
      } else {
        improve = calcScore(cut) - calcScore(cut + 1);
      }
    }

    public long calcScore() {
      return calcScore(cut);
    }

    public long calcScore(int cut) {
      int l1 = len / cut;
      if (len % cut == 0) {
        return l1 * 1L * l1 * cut;
      }
      int l2 = l1 + 1;
      int c2 = len % cut;
      int c1 = cut - c2;
      return l1 * 1L * l1 * c1 + l2 * 1L * l2 * c2;
    }

    @Override
    public int compareTo(Group o) {
      return Long.compare(o.improve, improve);
    }
  }

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

  void run() throws IOException {
    reader = new BufferedReader(new InputStreamReader(System.in));
//		reader = new BufferedReader(new FileReader("input.txt"));
    tokenizer = null;
    out = new PrintWriter(new OutputStreamWriter(System.out));
//		out = new PrintWriter(new FileWriter("output.txt"));
    solve();
    reader.close();
    out.flush();

  }

  BufferedReader reader;
  StringTokenizer tokenizer;
  PrintWriter out;

  int nextInt() throws IOException {
    return Integer.parseInt(nextToken());
  }

  long nextLong() throws IOException {
    return Long.parseLong(nextToken());
  }

  double nextDouble() throws IOException {
    return Double.parseDouble(nextToken());
  }

  String nextToken() throws IOException {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      tokenizer = new StringTokenizer(reader.readLine());
    }
    return tokenizer.nextToken();
  }
}
