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.
/*
    Case l<p is not needed, as, if l<p, then increase in cost is 0,
    so it will automatically not be selected.
 */

//created by Whiplash99
import java.io.*;
import java.util.*;
public class A
{
    private static long cost(int l, int p)
    {
        long w=l/p;
        long p2=l%p,p1=p-p2;

        return p1*(w*w)+p2*(w+1)*(w+1);
    }
    static class Pair implements Comparable<Pair>
    {
        int id, l, p;
        Pair(int id, int l, int p){this.id=id; this.l=l; this.p=p;}
        public int compareTo(Pair b)
        {
            long c1=cost(l,p)-cost(l,p+1);
            long c2=cost(b.l,b.p)-cost(b.l,b.p+1);

            return Long.compare(c1,c2);
        }
    }
    public static void main(String[] args) throws IOException
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));

        int i,N;

        String[] s=br.readLine().trim().split(" ");
        N=Integer.parseInt(s[0]);
        int K=Integer.parseInt(s[1]);

        int[] a=new int[N];
        s=br.readLine().trim().split(" ");
        for(i=0;i<N;i++) a[i]=Integer.parseInt(s[i]);

        PriorityQueue<Pair> PQ=new PriorityQueue<>(Collections.reverseOrder());
        for(i=0;i<N;i++)
            PQ.add(new Pair(i,a[i],1));

        int[] ans=new int[N];
        while (N++<K)
        {
            Pair tmp=PQ.poll();
            ans[tmp.id]++;
            if(N<K)  PQ.add(new Pair(tmp.id,tmp.l,tmp.p+1));
        }

        long minCost=0;
        for(i=0;i<a.length;i++) minCost+=cost(a[i],ans[i]+1);

        System.out.println(minCost);
    }
}