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.util.*;

public class Codeforces
{
    public static void main(String args[])throws Exception
    {
        BufferedReader bu=new BufferedReader(new InputStreamReader(System.in));
        StringBuilder sb=new StringBuilder();
        String s[]=bu.readLine().split(" ");
        int n=Integer.parseInt(s[0]),k=Integer.parseInt(s[1]);
        int i;
        s=bu.readLine().split(" ");
        PriorityQueue<Carrot> pq=new PriorityQueue<>(new Comparator<Carrot>() {
            @Override
            public int compare(Carrot o1, Carrot o2) {
                if(o1.a<o2.a) return 1;
                else if(o1.a==o2.a)
                {
                    if(o1.b<o2.b) return 1;
                    else if(o1.b==o2.b) return o1.c<=o2.c?1:-1;
                    else return -1;
                }
                else return -1;
            }});

        long sum=0;
        for(i=0;i<n;i++)
        {
            long x=Integer.parseInt(s[i]);
            sum+=x*x;
            pq.add(new Carrot(val(x,1)-val(x,2),x,2));
        }

        for(i=0;i<k-n;i++)
        {
            sum-=pq.peek().a;
            long a=pq.peek().b,b=pq.peek().c;
            pq.poll();
            pq.add(new Carrot(val(a,b)-val(a,b+1),a,b+1));
        }
        System.out.print(sum);
    }

    static class Carrot
    {
        long a,b,c;
        Carrot(long x,long y,long z)
        {
            a=x;
            b=y;
            c=z;
        }
    }

    static long val(long len,long n)
    {
        long unit=len/n,extra=len-unit*n;
        return (n-extra)*unit*unit+extra*(unit+1)*(unit+1);
    }


}