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 Practice {
  BufferedReader br;
  PrintWriter out;
  StringTokenizer st;
  boolean eof;
  private static final long MOD = 1000L * 1000L * 1000L + 7;
  private static final int[] dx = {0, -1, 0, 1};
  private static final int[] dy = {1, 0, -1, 0};
  private static final String yes = "Yes";
  private static final String no = "No";

  void solve() {
    int T = 1;
//    int T = nextInt();
    for (int i = 0; i < T; i++) {
      helper();
    }
  }

  void helper() {
    int n = nextInt();
    int k = nextInt();
    int[] arr = nextIntArr(n);
    PriorityQueue<Pair> pq = new PriorityQueue<>();
    for (int i = 0; i < n; i++) {
      pq.add(new Pair(arr[i], 1));
    }
    for (int i = 0; i < k - n; i++) {
      Pair cur = pq.poll();
      cur.cnt++;
      pq.add(cur);
    }
    long res = 0;
    for (Pair pair : pq) {
      res += calculate(pair.value, pair.cnt);
    }
    outln(res);
  }

  // Polls the biggest one.
  class Pair implements Comparable<Pair> {
    long value;
    int cnt;
    public Pair(long value, int cnt) {
      this.value = value;
      this.cnt = cnt;
    }

    @Override
    public int compareTo(Pair o) {
      long v1 = calcExtra(value, cnt);
      long v2 = calcExtra(o.value, o.cnt);
      if (v1 != v2) {
        return Long.compare(v2, v1);
      }
      if (value != o.value) {
        return Long.compare(value, o.value);
      }
      return Integer.compare(cnt, o.cnt);
    }

    @Override
    public String toString() {
      return value + " " + cnt;
    }
  }

  long calcExtra(long val, int cnt) {
    return calculate(val, cnt) - calculate(val, cnt + 1);
  }

  long calculate(long val, int cnt) {
    long res = 0;
    long avg = val / cnt;
    long rem = val % cnt;
    res += (cnt - rem) * avg * avg;
    res += rem * (avg + 1) * (avg + 1);
    return res;
  }

  void shuffle(long[] a) {
    int n = a.length;
    for(int i = 0; i < n; i++) {
      int r = i + (int) (Math.random() * (n - i));
      long tmp = a[i];
      a[i] = a[r];
      a[r] = tmp;
    }
  }
  long gcd(long a, long b) {
    while(a != 0 && b != 0) {
      long c = b;
      b = a % b;
      a = c;
    }
    return a + b;
  }
  private void outln(Object o) {
      out.println(o);
  }
  private void out(Object o) {
      out.print(o);
  }
  private void formatPrint(double val) {
      outln(String.format("%.9f%n", val));
  }
  public Practice() {
    br = new BufferedReader(new InputStreamReader(System.in));
    out = new PrintWriter(System.out);
    solve();
    out.close();
  }
  public static void main(String[] args) {
    new Practice();
  }

  public long[] nextLongArr(int n) {
    long[] res = new long[n];
    for(int i = 0; i < n; i++)
      res[i] = nextLong();
    return res;
  }
  public int[] nextIntArr(int n) {
    int[] res = new int[n];
    for(int i = 0; i < n; i++)
      res[i] = nextInt();
    return res;
  }
  public String nextToken() {
    while (st == null || !st.hasMoreTokens()) {
      try {
        st = new StringTokenizer(br.readLine());
      } catch (Exception e) {
        eof = true;
        return null;
      }
    }
    return st.nextToken();
  }
  public String nextString() {
    try {
      return br.readLine();
    } catch (IOException e) {
      eof = true;
      return null;
    }
  }
  public int nextInt() {
    return Integer.parseInt(nextToken());
  }
  public long nextLong() {
    return Long.parseLong(nextToken());
  }
  public double nextDouble() {
    return Double.parseDouble(nextToken());
  }
}