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.util.*;
import java.io.*;
public class EdE {
	static long num = 998244353;
	public static void main(String[] args) throws Exception{
		

		// TODO Auto-generated method stub
 		BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
 		PrintWriter out = new PrintWriter(System.out);
 		StringTokenizer st = new StringTokenizer(bf.readLine());
 		int n = Integer.parseInt(st.nextToken());
 		int k = Integer.parseInt(st.nextToken());
 		PriorityQueue<Pair> pq = new PriorityQueue<Pair>();
 		StringTokenizer st1 = new StringTokenizer(bf.readLine());
 		for(int j =0;j<n;j++){
 			int number = Integer.parseInt(st1.nextToken());
 			pq.add(new Pair(number, 1));
 		}
 		for(int j = 0;j<k-n;j++){
 			Pair nu = pq.remove();
 			Pair p = new Pair(nu.number, nu.priority+1);
 			pq.add(p);
 		}
 		
 		long sum = 0;
 		while(!pq.isEmpty()){
 			Pair ns = pq.remove();
 			sum+=(long)(ns.totalDiff(ns.priority));
 		}
 		
 		
 		out.println(sum);
	 		
 		out.close();
 		
 		
 		
 	}
	static class Pair implements Comparable<Pair>{
		private int number;
		private int priority;
		public Pair(int number, int priority){
			this.number = number;
			this.priority = priority;
		}
		public int compareTo(Pair other){
			long val1 = totalDiff(priority)-totalDiff(priority+1);
			long val2 = other.totalDiff(other.priority) - other.totalDiff(other.priority+1);
			return Long.compare(val2,  val1);
		}
		public long totalDiff(int priority){
			int one = number%priority;
			int zero = priority-number%priority;
			
			return (long)(zero)*(long)(number/priority)*(long)(number/priority) + (long)(one)*(long)(number/priority+1)*(long)(number/priority+1);
		}
	}
}
 	
 
//StringJoiner sj = new StringJoiner(" "); 
//sj.add(strings)
//sj.toString() gives string of those stuff w spaces or whatever that sequence is

 		
 		
 		
 		
	


