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.*;
import java.math.*;
 
//Sub_To_Errichto
public class Main {
    static final long MOD = 1000000007L;
    //static final long MOD = 998244353L;
    static final int INF = 50000000;
    static final int NINF = -500000000;

    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        PrintWriter pw = new PrintWriter(System.out);
        
    	int N = sc.ni();
    	int K = sc.ni();
        PriorityQueue<Input> pq = new PriorityQueue<Input>();
    	for (int i = 0; i < N; i++) {
    		pq.add(new Input(sc.nl()));
    	}
    	
    	
    	while (K > N) {
    		Input e = pq.poll();
    		e.update();
    		pq.add(e);
    		K--;
    	}
    	long ans = 0;
    	while (!pq.isEmpty()) {
    		Input e = pq.poll();
    		ans += e.calc(e.p);
    	}
    	pw.println(ans);
    	pw.close();
    }
    
    static class Input implements Comparable<Input> {
    	long num;
    	int p;
    	long save;
    	public Input(long n) {
    		num = n;
    		p = 1;
    		save = calc(p)-calc(p+1);
    	}
    	
    	public void update() {
    		p++;
    		save = calc(p)-calc(p+1);
    	}
    	
    	public int compareTo(Input e) {
    		if (save > e.save)
    			return -1;
    		else if (save < e.save)
    			return 1;
    		else
    			return 0;
    	}
    	
    	public long calc(int pc) {
    		long div = num/pc;
    		long v = (pc-(num%pc));
    		long ans = v*div*div + (pc-v)*(div+1)*(div+1);
    		return ans;
    	}
    	
    	public String toString() {
    		return "["+num+","+p+","+save+"]";
    	}
    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
 
        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
 
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int ni() {
            return Integer.parseInt(next());
        }
 
        long nl() {
            return Long.parseLong(next());
        }
 
        double nd() {
            return Double.parseDouble(next());
        }
 
        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}