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 e {
    public static PrintWriter out;
    public static void main(String[] Args) throws Exception{
        FS sc = new FS(System.in);
        out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        int n = sc.nextInt();
        int k = sc.nextInt()-n;
        PriorityQueue<Thing> pq = new PriorityQueue<Thing>();
        long ans = 0;
        for (int i = 0; i < n; i++) {
            Thing nT = new Thing(sc.nextInt());
            ans += nT.w;
            pq.add(nT);
        }
        while (k-->0) {
            Thing cur = pq.poll();
            ans -= cur.w;
            cur.split();
            ans += cur.w;
            pq.add(cur);
        }
        out.println(ans);
        out.close();
    }   
    public static class Thing implements Comparable<Thing> {
        long w;
        long sortVal;
        int cuts;
        long total;
        Thing(int val) {
            total = val;
            cuts = 1;
            w = val;
            w = w * w;
            sortVal = getNextW() - w;
        }
        long getNextW() {
            int newCuts = cuts + 1;
            long small = total / newCuts;
            long big = small + 1;
            long bigC = total % newCuts;
            long smallC = newCuts - bigC;
            return (smallC * small * small + bigC * big * big);
        }
        void split() {
            w = getNextW();
            cuts++;
            sortVal = getNextW() - w;
        }
        public int compareTo(Thing o) {
            return Long.compare(sortVal, o.sortVal);
        }
    }
    public static class FS {
        BufferedReader br;
        StringTokenizer st;
        FS(InputStream in) throws Exception {
            br = new BufferedReader(new InputStreamReader(in));
            st = new StringTokenizer(br.readLine());
        }
        String next() throws Exception {
            if (st.hasMoreTokens())
                return st.nextToken();
            st = new StringTokenizer(br.readLine());
            return next();
        }
        int nextInt() throws Exception {
            return Integer.parseInt(next());
        }
        long nextLong() throws Exception {
            return Long.parseLong(next());
        }
    } 
}