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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.PriorityQueue;
import java.util.*;

public class Main
{
	public static void main(String[] args) {
		new Thread(null, new Runnable() {
			public void run() {
                solve();
            }
        }, "1", 1 << 26).start();
	}
	static void solve () {
		FastReader fr =new FastReader();	PrintWriter op =new PrintWriter(System.out);
 
 		int n =fr.nextInt() ,k =fr.nextInt() ,carrot[][] =new int[n][2] ,cut =k-n ,i ;

 		PriorityQueue<pair> pq =new PriorityQueue<>(n , new cmp()) ;

 		long j ,sum =0 ;

 		pair obj ;

 		for (i =0 ; i<n ; ++i) {
 			carrot[i][0] =fr.nextInt() ;

 			carrot[i][1] =1 ;

 			j =findTime(carrot[i][0] , carrot[i][1]) - findTime(carrot[i][0] , carrot[i][1]+1) ;

 			pq.add(new pair(j , i)) ;
 		}

 		while (cut-- > 0) {
 			obj =pq.poll() ;

 			i =obj.second ;

 			++carrot[i][1] ;

 			j =findTime(carrot[i][0] , carrot[i][1]) - findTime(carrot[i][0] , carrot[i][1]+1) ;

 			obj.first =j ;

 			pq.add(obj) ;
 		}

 		for (i =0 ; i<n ; ++i) {
 			j =findTime(carrot[i][0] , carrot[i][1]) ;

 			sum += j ;
 		}

		op.println(sum) ;	op.flush();	op.close();
	}
	static long findTime (long L , long P) {
		long w =L/P ,P2 =L%P ;

		long time =(w*w) * (P - P2) ;

		++w ;

		time += ((w*w) * P2) ;

		return time ;
	}
	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			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();
		}

		String nextLine() {
			String str ="";

			try
			{
				str =br.readLine();
			}
			catch(IOException e)
			{
				e.printStackTrace();
			}

			return str;
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next()) ;
		}
	}
}
class pair {
	long first ;

	int second ;

	pair (long f , int s) {
		first =f ;

		second =s ;
	}
}
class cmp implements Comparator<pair> {
	public int compare (pair A , pair B) {
		long diff =B.first - A.first ;

		if (diff == 0)	return 0 ;

		if (diff < 0)	return -1 ;

		return 1 ;
	}
}