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.StringTokenizer;

/*
break case
optimalDivision(28,8) returns 112 should return 100 (optimal is 3,3,3,3,4,4,4,4)
*/

public class e2 {
	public static void main(String[] args) {
		FastScanner scan=new FastScanner();
		PrintWriter out=new PrintWriter(System.out);
		
		int n=scan.nextInt(), k=scan.nextInt();
		PriorityQueue<carrot> q=new PriorityQueue<>();
		
		for(int i=0;i<n;i++) q.offer(new carrot(scan.nextLong(),1));
		
//		System.out.println(q);
		long res=0L;
		
		while(!q.isEmpty()&&k-n>0) {
			carrot c=q.poll();
			q.offer(new carrot(c.len,c.pieces+1));
			k--;
		}
		
		for(carrot c:q) res+=c.sqsum;
		
		out.println(res);
		out.close();
	}
	
	public static long optimalDivision(long len, long pieces) {
		long res=Long.MAX_VALUE;
		long div=len/pieces, rem=len%pieces;
		//distribute the rem among the others evenly
		//rem numbers will be equal to div+1
		//the other pieces-rem numbers will be equal to div
		
		return rem*(div+1)*(div+1)+(pieces-rem)*(div)*(div);
	}
	
	static class carrot implements Comparable<carrot> {
		long len,pieces;
		long sqsum;
		long sqdelta;
		
		carrot(long len, long pieces) {
			this.len=len;
			this.pieces=pieces;
			sqsum=optimalDivision(len,pieces);
			sqdelta=calcdelta();
		}
		
		long calcdelta() {
			if(len==pieces) return -1;
			
			long nxt=optimalDivision(len,pieces+1);
			return sqsum-nxt;
		}
		
		@Override
		public int compareTo(carrot o) {
			return Long.compare(o.sqdelta,sqdelta);
		}
		public String toString() {
			return len+" "+pieces+" "+sqsum+" "+sqdelta;
		}
	}
	static class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		public FastScanner() {
			try	{
				br = new BufferedReader(new InputStreamReader(System.in));
				st = new StringTokenizer(br.readLine());
			} catch (Exception e){e.printStackTrace();}
		}

		public String next() {
			if (st.hasMoreTokens())	return st.nextToken();
			try {st = new StringTokenizer(br.readLine());}
			catch (Exception e) {e.printStackTrace();}
			return st.nextToken();
		}

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

		public long nextLong() {return Long.parseLong(next());}

		public double nextDouble() {return Double.parseDouble(next());}

		public String nextLine() {
			String line = "";
			if(st.hasMoreTokens()) line = st.nextToken();
			else try {return br.readLine();}catch(IOException e){e.printStackTrace();}
			while(st.hasMoreTokens()) line += " "+st.nextToken();
			return line;
		}
	}
}
/*
break case
1 3
7
prints 19 should print 17

break case 2
2 5
6 6
prints 32 should print 30
*/