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.*;
import java.util.*;

import static java.lang.Math.*;
import static java.util.Arrays.*;

public class cf1328f {

    public static void main(String[] args) throws IOException {
        int n = rni(), k = ni(), a[] = ria(n);
        Map<Integer, Long> cnt = new TreeMap<>();
        for(int i : a) {
            cnt.put(i, cnt.getOrDefault(i, 0L) + 1);
            if(cnt.get(i) == k) {
                prln(0);
                close();
                return;
            }
        }
        Iterator<Integer> l = cnt.keySet().iterator();
        int curl = l.next();
        long lcost = 0, rcost = 0, lnum = 0, rnum = n - cnt.get(curl), ans;
        for(int i : cnt.keySet()) {
            rcost += cnt.get(i) * max(0, i - curl - 1);
        }
        ans = rcost + k - cnt.get(curl);
        while(l.hasNext()) {
            int nextl = l.next();
            lcost += lnum * (nextl - curl) + cnt.get(curl) * (nextl - curl - 1);
            lnum += cnt.get(curl);
            rcost -= (rnum - cnt.get(nextl)) * (nextl - curl) + cnt.get(nextl) * (nextl - curl - 1);
            rnum -= cnt.get(nextl);
            // prln(nextl, lcost, lnum, rcost, rnum);
            long curcost = LMAX;
            if(lcost <= rcost) {
                if(lnum < k - cnt.get(nextl)) {
                    if(rnum >= k - cnt.get(nextl)) {
                        curcost = rcost + k - cnt.get(nextl);
                    }
                    curcost = min(curcost, lcost + rcost + k - cnt.get(nextl));
                } else {
                    curcost = lcost + k - cnt.get(nextl);
                }
            } else {
                if(rnum < k - cnt.get(nextl)) {
                    if(lnum >= k - cnt.get(nextl)) {
                        curcost = lcost + k - cnt.get(nextl);
                    }
                    curcost = min(curcost, lcost + rcost + k - cnt.get(nextl));
                } else {
                    curcost = rcost + k - cnt.get(nextl);
                }
            }
            curl = nextl;
            // prln(curcost);
            ans = min(ans, curcost);
        }
        prln(ans);
        close();
    }

    static BufferedReader __in = new BufferedReader(new InputStreamReader(System.in));
    static PrintWriter __out = new PrintWriter(new OutputStreamWriter(System.out));
    static StringTokenizer input;
    static Random rand = new Random();

    // references
    // IBIG = 1e9 + 7
    // IMAX ~= 2e10
    // LMAX ~= 9e18
    
    // constants
    static final int IBIG = 1000000007;
    static final int IMAX = 2147483647;
    static final int IMIN = -2147483648;
    static final long LMAX = 9223372036854775807L;
    static final long LMIN = -9223372036854775808L;
    // math util
    static int minof(int a, int b, int c) {return min(a, min(b, c));}
    static int minof(int... x) {if(x.length == 1) return x[0]; if(x.length == 2) return min(x[0], x[1]); if(x.length == 3) return min(x[0], min(x[1], x[2])); int min = x[0]; for(int i = 1; i < x.length; ++i) if(x[i] < min) min = x[i]; return min;}
    static long minof(long a, long b, long c) {return min(a, min(b, c));}
    static long minof(long... x) {if(x.length == 1) return x[0]; if(x.length == 2) return min(x[0], x[1]); if(x.length == 3) return min(x[0], min(x[1], x[2])); long min = x[0]; for(int i = 1; i < x.length; ++i) if(x[i] < min) min = x[i]; return min;}
    static int maxof(int a, int b, int c) {return max(a, max(b, c));}
    static int maxof(int... x) {if(x.length == 1) return x[0]; if(x.length == 2) return max(x[0], x[1]); if(x.length == 3) return max(x[0], max(x[1], x[2])); int max = x[0]; for(int i = 1; i < x.length; ++i) if(x[i] > max) max = x[i]; return max;}
    static long maxof(long a, long b, long c) {return max(a, max(b, c));}
    static long maxof(long... x) {if(x.length == 1) return x[0]; if(x.length == 2) return max(x[0], x[1]); if(x.length == 3) return max(x[0], max(x[1], x[2])); long max = x[0]; for(int i = 1; i < x.length; ++i) if(x[i] > max) max = x[i]; return max;}
    static int powi(int a, int b) {if(a == 0) return 0; int ans = 1; while(b > 0) {if((b & 1) > 0) ans *= a; a *= a; b >>= 1;} return ans;}
    static long powl(long a, int b) {if(a == 0) return 0; long ans = 1; while(b > 0) {if((b & 1) > 0) ans *= a; a *= a; b >>= 1;} return ans;}
    static int floori(double d) {return (int)d;}
    static int ceili(double d) {return (int)ceil(d);}
    static long floorl(double d) {return (long)d;}
    static long ceill(double d) {return (long)ceil(d);}
    static int randInt(int min, int max) {return rand.nextInt(max - min + 1) + min;}
    // array util
    static void reverse(int[] a) {for(int i = 0, n = a.length, half = n / 2; i < half; ++i) {int swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void reverse(long[] a) {for(int i = 0, n = a.length, half = n / 2; i < half; ++i) {long swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void reverse(double[] a) {for(int i = 0, n = a.length, half = n / 2; i < half; ++i) {double swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void reverse(char[] a) {for(int i = 0, n = a.length, half = n / 2; i < half; ++i) {char swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static <T> void reverse(T[] a) {for(int i = 0, n = a.length, half = n / 2; i < half; ++i) {T swap = a[i]; a[i] = a[n - i - 1]; a[n - i - 1] = swap;}}
    static void shuffle(int[] a) {int n = a.length - 1; for(int i = 0; i < n; ++i) {int ind = randInt(i, n); int swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
    static void shuffle(long[] a) {int n = a.length - 1; for(int i = 0; i < n; ++i) {int ind = randInt(i, n); long swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
    static void shuffle(double[] a) {int n = a.length - 1; for(int i = 0; i < n; ++i) {int ind = randInt(i, n); double swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
    static void shuffle(char[] a) {int n = a.length - 1; for(int i = 0; i < n; ++i) {int ind = randInt(i, n); char swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
    static <T> void shuffle(T[] a) {int n = a.length - 1; for(int i = 0; i < n; ++i) {int ind = randInt(i, n); T swap = a[i]; a[i] = a[ind]; a[ind] = swap;}}
    static void rsort(int[] a) {shuffle(a); sort(a);}
    static void rsort(long[] a) {shuffle(a); sort(a);}
    static void rsort(double[] a) {shuffle(a); sort(a);}
    static void rsort(char[] a) {shuffle(a); sort(a);}
    static <T> void rsort(T[] a) {shuffle(a); sort(a);}
    // graph util
    static List<List<Integer>> graph(int n) {List<List<Integer>> g = new ArrayList<>(); for(int i = 0; i < n; ++i) g.add(new ArrayList<>()); return g;}
    static void connect(List<List<Integer>> g, int u, int v) {g.get(u).add(v); g.get(v).add(u);}
    static void connectDirected(List<List<Integer>> g, int u, int v) {g.get(u).add(v);};
    // input
    static void r() throws IOException {input = new StringTokenizer(__in.readLine());}
    static int ri() throws IOException {return Integer.parseInt(__in.readLine());}
    static long rl() throws IOException {return Long.parseLong(__in.readLine());}
    static int[] ria(int n) throws IOException {int[] a = new int[n]; input = new StringTokenizer(__in.readLine()); for(int i = 0; i < n; ++i) a[i] = Integer.parseInt(input.nextToken()); return a;}
    static int[] riam1(int n) throws IOException {int[] a = new int[n]; input = new StringTokenizer(__in.readLine()); for(int i = 0; i < n; ++i) a[i] = Integer.parseInt(input.nextToken()) - 1; return a;}
    static long[] rla(int n) throws IOException {long[] a = new long[n]; input = new StringTokenizer(__in.readLine()); for(int i = 0; i < n; ++i) a[i] = Long.parseLong(input.nextToken()); return a;}
    static char[] rcha() throws IOException {return __in.readLine().toCharArray();}
    static String rline() throws IOException {return __in.readLine();}
    static int rni() throws IOException {input = new StringTokenizer(__in.readLine()); return Integer.parseInt(input.nextToken());}
    static int ni() {return Integer.parseInt(input.nextToken());}
    static long rnl() throws IOException {input = new StringTokenizer(__in.readLine()); return Long.parseLong(input.nextToken());}
    static long nl() {return Long.parseLong(input.nextToken());}
    // output
    static void pr(int i) {__out.print(i);}
    static void prln(int i) {__out.println(i);}
    static void pr(long l) {__out.print(l);}
    static void prln(long l) {__out.println(l);}
    static void pr(double d) {__out.print(d);}
    static void prln(double d) {__out.println(d);}
    static void pr(char c) {__out.print(c);}
    static void prln(char c) {__out.println(c);}
    static void pr(char[] s) {__out.print(new String(s));}
    static void prln(char[] s) {__out.println(new String(s));}
    static void pr(String s) {__out.print(s);}
    static void prln(String s) {__out.println(s);}
    static void pr(Object o) {__out.print(o);}
    static void prln(Object o) {__out.println(o);}
    static void prln() {__out.println();}
    static void pryes() {__out.println("yes");}
    static void pry() {__out.println("Yes");}
    static void prY() {__out.println("YES");}
    static void prno() {__out.println("no");}
    static void prn() {__out.println("No");}
    static void prN() {__out.println("NO");}
    static void pryesno(boolean b) {__out.println(b ? "yes" : "no");};
    static void pryn(boolean b) {__out.println(b ? "Yes" : "No");}
    static void prYN(boolean b) {__out.println(b ? "YES" : "NO");}
    static void prln(int... a) {for(int i = 0, len = a.length - 1; i < len; __out.print(a[i]), __out.print(' '), ++i); __out.println(a[a.length - 1]);}
    static void prln(long... a) {for(int i = 0, len = a.length - 1; i < len; __out.print(a[i]), __out.print(' '), ++i); __out.println(a[a.length - 1]);}
    static <T> void prln(Collection<T> c) {int n = c.size() - 1; Iterator<T> iter = c.iterator(); for(int i = 0; i < n; __out.print(iter.next()), __out.print(' '), ++i); __out.println(iter.next());}
    static void h() {__out.println("hlfd");}
    static void flush() {__out.flush();}
    static void close() {__out.close();}
}