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.
/*
    Java might be good for Competitive Programming but Python still rocks!!!!!!!!!


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*/


import java.util.*;
import java.lang.*;
import java.io.*;
public final class ProblemE
{
    public static BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
    public static int t, n, i, j, k, u, v;
    public static void main(String[] args) throws IOException
    {
        FastScanner sc = new FastScanner();
        Print print = new Print();
        n = sc.nextInt();
        k = sc.nextInt();
        long answer = 0;
        PriorityQueue<Node> q = new PriorityQueue<>();
        Node node;
        for(i = 0; i < n; i++)
            q.add(new Node(sc.nextInt(), 1));
        for(i = 0; i < k - n; i++)
        {
            node = q.poll();
            node.b++;
            q.add(node);
        }
        while(!q.isEmpty())
        {
            node = q.poll();
            answer += node.calculate(node.b);
        }
        out.write(answer+"");
        out.flush();
        out.close();
    }

    static class Node implements Comparable<Node> {
        int ele, b;
        Node(int ele, int b)
        {
            this.ele = ele;
            this.b = b;
        }

        long calculate(int a)
        {
            long quo = this.ele / a;
            long rem = this.ele % a;
            return quo * quo * (a - rem) + (quo + 1) * (quo + 1) * rem;
        }

        @Override
        public int compareTo(Node o)
        {
            return Long.compare(o.calculate(o.b) - o.calculate(o.b + 1),
                    this.calculate(this.b) - this.calculate(this.b + 1));
        }
    }

    public static class Print
    {
        Print()
        {}

        void integer(int... arr) throws IOException
        {
            for(int value: arr)
            {
                out.write(value+" ");
                out.flush();
            }
            out.write("\n");
            out.flush();
        }

        void string(String... arr) throws IOException
        {
            for(String value: arr)
            {
                out.write(value+" ");
                out.flush();
            }
            out.write("\n");
            out.flush();
        }

        void character(char... arr) throws IOException
        {
            for(char value: arr)
            {
                out.write(value+" ");
                out.flush();
            }
            out.write("\n");
            out.flush();
        }

        void long_int(long... arr) throws IOException
        {
            for(long value: arr)
            {
                out.write(value+" ");
                out.flush();
            }
            out.write("\n");
            out.flush();
        }
    }

    static class FastScanner
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        String next()
        {
            while (!st.hasMoreTokens())
                try
                {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e)
                {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }
        int[] readArray(int n)
        {
            int[] a=new int[n];
            for (int i=0; i<n; i++) a[i]=nextInt();
            return a;
        }
        long nextLong()
        {
            return Long.parseLong(next());
        }
    }
}
