Problem: You are given the array a consisting of n elements and the integer k ≤ n.

You want to obtain at least k equal elements in the array a. In one move, you can make one of the following two operations:

  * Take one of the minimum elements of the array and increase its value by one (more formally, if the minimum value of a is mn then you choose such index i that a_i = mn and set a_i := a_i + 1); 
  * take one of the maximum elements of the array and decrease its value by one (more formally, if the maximum value of a is mx then you choose such index i that a_i = mx and set a_i := a_i - 1). 



Your task is to calculate the minimum number of moves required to obtain at least k equal elements in the array.

Input

The first line of the input contains two integers n and k (1 ≤ k ≤ n ≤ 2 ⋅ 10^5) — the number of elements in a and the required number of equal elements.

The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9), where a_i is the i-th element of a.

Output

Print one integer — the minimum number of moves required to obtain at least k equal elements in the array.

Examples

Input


6 5
1 2 2 4 2 3


Output


3


Input


7 5
3 3 2 1 1 1 3


Output


4

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class Main {
    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner();
        PrintWriter out = new PrintWriter(System.out);
        int n = sc.nextInt(), k = sc.nextInt();
        int[] a = sc.nextIntArray(n);
        int ans = -1;
        int max = (int) (2e5 + 1);
        TreeMap<Integer, Integer> cnt[] = new TreeMap[max];
        for (int i = 0; i < max; i++)
            cnt[i] = new TreeMap<>();
        for (int x : a) {
            int tmp = x;
            cnt[x].put(0, cnt[x].getOrDefault(0, 0) + 1);
            int steps = 0;
            while (tmp > 0) {
                tmp >>= 1;
                steps++;
                cnt[tmp].put(steps, cnt[tmp].getOrDefault(steps, 0) + 1);
            }
        }
        for (TreeMap<Integer, Integer> map : cnt) {
            int cand = 0;
            int cur = k;
            for (int steps : map.keySet()) {
                int occ = map.get(steps);
                int take = Math.min(cur, occ);
                cand += take * steps;
                cur -= take;
                if (cur == 0) break;
            }
            if (cur != 0) continue;
            if (ans == -1 || ans > cand) ans = cand;
        }
        out.println(ans);
        out.flush();
        out.close();
    }


    static class Scanner {
        BufferedReader br;
        StringTokenizer st;

        Scanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

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

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

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

        int[] nextIntArray(int n) throws IOException {
            int[] ans = new int[n];
            for (int i = 0; i < n; i++)
                ans[i] = nextInt();
            return ans;
        }

    }


}