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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.PriorityQueue;
import java.util.Random;
import java.util.StringTokenizer;

public class Main {

static class Carrot implements Comparable<Carrot>{
	int length, cuts;
	public Carrot(int length, int cuts) {
		this.length = length;
		this.cuts = cuts;
	}
	
	private long cutProfit() {
		return time(cuts) - time(cuts + 1);
	}

	private long time(int x) {
		if(x == -1) x = cuts;
		// how much time will x cuts take
		x++;
		int first = length / x;
		int rem = length - first * x;
		long ans = 1l * rem * square(first + 1) + 1l * (x - rem) * square(first);
		return ans;
	}

	@Override
	public int compareTo(Carrot o) {
		return Long.compare(cutProfit(), o.cutProfit());
	}
}
	
	
public static void main(String[] args){
 
   new Thread(null, null, "Anshum Gupta", 99999999) {
        public void run() {
            try {
                solve();
            } catch(Exception e) {
                e.printStackTrace();
                System.exit(1);
            }
        }
    }.start();
}
 
static final long mxx = (long)(1e18 + 5), MOD = 998244353;
static final int mxN = (int)(1e6), mxV = (int)(1e6), log = 18, INF = (int)1e9;
static boolean[]vis;
static ArrayList<ArrayList<Integer>> adj = new ArrayList<ArrayList<Integer>>();
static int n, m, q, k;
static char[]str;
static PriorityQueue<Carrot> pq;

public static void solve() throws Exception {
	   // solve the problem here
		s = new MyScanner();
   		out = new PrintWriter(new BufferedOutputStream(System.out), true);
//	   		out = new PrintWriter("output.txt");
        int tc = 1;//s.nextInt();   	
    	for(int i=1; i<=tc; i++) {
//        	out.print("Case #" + i + ": ");
    		testcase();
    	}
          
        out.flush();
        out.close();
}



static void testcase() {
	n = s.nextInt();
	k = s.nextInt();
	int[] a = s.nextIntArray(n);
	pq = new PriorityQueue<>(Collections.reverseOrder());
	for(int i = 0; i < n; i++) {
		pq.add(new Carrot(a[i], 0));
	}
	
	for(int i = 0; i < k - n; i++) {
		// make a cut
		Carrot best = pq.poll();
		best.cuts++;
		pq.add(best);
	}
	long ans = 0;
	while(!pq.isEmpty()) {
		ans += pq.poll().time(-1);
	}
	
	out.println(ans);
}


private static long square(int x) {
	return 1l * x * x;
}

public static PrintWriter out;
public static MyScanner s;
static void shuffleArray(int[] a) {
	Random random = new Random();
	for (int i = a.length-1; i > 0; i--) {
		int index = random.nextInt(i + 1);
		int tmp = a[index];
		a[index] = a[i];
		a[i] = tmp;
	}
}
static void shuffleSort(int[] a) {
	shuffleArray(a);
	Arrays.parallelSort(a);
}
static class MyScanner {
 
    BufferedReader br;
    StringTokenizer st;
 
    public MyScanner() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }
    public MyScanner(String fileName) {
    	try {
			br = new BufferedReader(new FileReader(fileName));
		} catch (FileNotFoundException e) {
			e.printStackTrace();
		}
    }
    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }
 
    int nextInt() { return Integer.parseInt(next()); }
    long nextLong() { return Long.parseLong(next()); }
    double nextDouble() { return Double.parseDouble(next()); }
    int[] nextIntArray(int n){
    	int[]a = new int[n];
    	for(int i=0; i<n; i++) {
    		a[i] = this.nextInt();
    	}
    	return a;
    }
    long[] nextlongArray(int n) {
    	long[]a = new long[n];
    	for(int i=0; i<n; i++) {
    		a[i] = this.nextLong();
    	}
    	return a;
    }
    Integer[] nextIntegerArray(int n){
    	Integer[]a = new Integer[n];
    	for(int i=0; i<n; i++) {
    		a[i] = this.nextInt();
    	}
    	return a;
    }
    Long[] nextLongArray(int n) {
    	Long[]a = new Long[n];
    	for(int i=0; i<n; i++) {
    		a[i] = this.nextLong();
    	}
    	return a;
    }
    char[][] next2DCharArray(int n, int m){
    	char[][]arr = new char[n][m];
    	for(int i=0; i<n; i++) {
    		arr[i] = this.next().toCharArray();
    	}
    	return arr;
    }
    ArrayList<ArrayList<Integer>> readUndirectedUnweightedGraph(int n, int m) {
    	ArrayList<ArrayList<Integer>>adj = new ArrayList<ArrayList<Integer>>();
    	for(int i=0; i<=n; i++)adj.add(new ArrayList<Integer>());
    	for(int i=0; i<m; i++) {
    		int u = s.nextInt();
    		int v = s.nextInt();
    		adj.get(u).add(v);
    		adj.get(v).add(u);
    	}
    	return adj;
    }
    ArrayList<ArrayList<Integer>> readDirectedUnweightedGraph(int n, int m) {
    	ArrayList<ArrayList<Integer>>adj = new ArrayList<ArrayList<Integer>>();
    	for(int i=0; i<=n; i++)adj.add(new ArrayList<Integer>());
    	for(int i=0; i<m; i++) {
    		int u = s.nextInt();
    		int v = s.nextInt();
    		adj.get(u).add(v);
    	}
    	return adj;
    }
    String nextLine(){
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
}
 
 
}