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 E {
    public static void main(String[] args) throws IOException{
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
        StringTokenizer st = new StringTokenizer(f.readLine());
        int n = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());
        long sum = 0;
        TreeMap<Pair, Integer> nums = new TreeMap<Pair, Integer>();
        st = new StringTokenizer(f.readLine());
        for(int i = 0; i < n; i++){
            long temp = Long.parseLong(st.nextToken());
            update(nums, new Pair(temp, 1), true);
            sum+=(temp*temp);
        }

        for(int i = n; i < k; i++){
            Pair last = nums.lastKey();
            update(nums, last, false);
            sum-=last.index;
            update(nums, new Pair(last.a, last.b+1), true);
        }

        out.println(sum);
        out.close();


    }
    public static void update(TreeMap<Pair, Integer> map, Pair elem, boolean add){
        if(add){
            if(!map.containsKey(elem)) map.put(elem, 0);
            map.put(elem, map.get(elem)+1);
        }else{
            map.put(elem, map.get(elem)-1);
            if(map.get(elem) == 0) map.remove(elem);
        }
    }
    static class Pair implements Comparable<Pair>{
        public long a;
        public long b;
        public long index;
        public Pair(long a, long b){
            this.a=a;
            this.b=b;
            long val1 = a/b;
            long val2 = a%b;
            long val3 = a/(b+1);
            long val4 = a%(b+1);
            index = ((b-val2)*(val1)*val1 + val2*(val1+1)*(val1+1)) - ((b+1-val4)*(val3)*val3 + val4*(val3+1)*(val3+1));
        }

        public int compareTo(Pair p){
            if(index > p.index) return 1;
            if(index < p.index) return -1;
            if(a < p.a) return -1;
            if(a > p.a) return 1;
            if(b < p.b) return -1;
            if(b > p.b) return 1;
            return 0;
        }
    }
}
