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.util.*;
import java.io.*;
import java.math.*;

/**
 *
 * @Har_Har_Mahadev
 */

public class F {

	private static long INF = 2000000000000000000L, M = 1000000007, MM = 998244353;
	

	public static void process() throws IOException {
		int n = sc.nextInt();
		int k = sc.nextInt();
		long a[] = sc.readArrayLong(n);
		
		HashSet<Long> set=new HashSet<>();
        HashMap<Long,Integer> map=new HashMap<>();
        int i = 0;
        for(i=0;i<n;i++)
        {
            set.add(a[i]);
            map.put(a[i],map.getOrDefault(a[i],0)+1);
        }
        
        n=set.size(); i=0;
        Arrays.fill(a,0);
        for(long tmp:set) a[i++]=tmp;
        Arrays.sort(a,0,n);
        
        long prefix[]=new long[n+1];
        int count[]=new int[n+1];
        for(i=1;i<=n;i++) prefix[i]=prefix[i-1]+a[i-1]*map.get(a[i-1]);
        for(i=1;i<=n;i++) count[i]=count[i-1]+map.get(a[i-1]);
        
        long ans=INF;
        
        for(i=0;i<n;i++)
        {
            int needed=k-map.get(a[i]);
            long lCount=0,rCount=0;
            int lExist=count[i],rExist=count[n]-count[i+1];
 
            if(needed<=0) {ans=0;break;}
            
            if(lExist>0) lCount=lExist*(a[i]-1)-prefix[i];
            if(rExist>0) rCount=prefix[n]-prefix[i+1]-(rExist)*(a[i]+1);
 
            if(lExist>=needed) ans=Math.min(ans,lCount+needed);
            if(rExist>=needed) ans=Math.min(ans,rCount+needed);
            ans=Math.min(ans,lCount+rCount+needed);
        }
        System.out.println(ans);
		

	}

	//=============================================================================
	//--------------------------The End---------------------------------
	//=============================================================================

	static FastScanner sc;
	static PrintWriter out;

	public static void main(String[] args) throws IOException {
		boolean oj = true;
		if (oj) {
			sc = new FastScanner();
			out = new PrintWriter(System.out);
		} else {
			sc = new FastScanner(100);
			out = new PrintWriter("output.txt");
		}
		int t = 1;
//		t = sc.nextInt();
		while (t-- > 0) {
			process();
		}
		out.flush();
		out.close();
	}

	static class Pair implements Comparable<Pair> {
		int x, y;

		Pair(int x, int y) {
			this.x = x;
			this.y = y;
		}

		@Override
		public int compareTo(Pair o) {
			return Integer.compare(this.x, o.x);
		}

		//		 @Override
		//		    public boolean equals(Object o) {
		//		        if (this == o) return true;
		//		        if (!(o instanceof Pair)) return false;
		//		        Pair key = (Pair) o;
		//		        return x == key.x && y == key.y;
		//		    }
		//		 
		//		    @Override
		//		    public int hashCode() {
		//		        int result = x;
		//		        result = 31 * result + y;
		//		        return result;
		//		    }
	}

	/////////////////////////////////////////////////////////////////////////////////////////////////////////

	static void println(Object o) {
		out.println(o);
	}

	static void println() {
		out.println();
	}

	static void print(Object o) {
		out.print(o);
	}

	static void pflush(Object o) {
		out.println(o);
		out.flush();
	}

	static int ceil(int x, int y) {
		return (x % y == 0 ? x / y : (x / y + 1));
	}

	static long ceil(long x, long y) {
		return (x % y == 0 ? x / y : (x / y + 1));
	}

	static int max(int x, int y) {
		return Math.max(x, y);
	}

	static int min(int x, int y) {
		return Math.min(x, y);
	}

	static int abs(int x) {
		return Math.abs(x);
	}

	static long abs(long x) {
		return Math.abs(x);
	}

	static int log2(int N) {
		int result = (int) (Math.log(N) / Math.log(2));
		return result;
	}

	static long max(long x, long y) {
		return Math.max(x, y);
	}

	static long min(long x, long y) {
		return Math.min(x, y);
	}

	public static int gcd(int a, int b) {
		BigInteger b1 = BigInteger.valueOf(a);
		BigInteger b2 = BigInteger.valueOf(b);
		BigInteger gcd = b1.gcd(b2);
		return gcd.intValue();
	}

	public static long gcd(long a, long b) {
		BigInteger b1 = BigInteger.valueOf(a);
		BigInteger b2 = BigInteger.valueOf(b);
		BigInteger gcd = b1.gcd(b2);
		return gcd.longValue();
	}

	public static long lcm(long a, long b) {
		return (a * b) / gcd(a, b);
	}

	public static int lcm(int a, int b) {
		return (a * b) / gcd(a, b);
	}

	public static int lower_bound(int[] arr, int x) {
		int low = 0, high = arr.length, mid = -1;

		while (low < high) {
			mid = (low + high) / 2;

			if (arr[mid] >= x)
				high = mid;
			else
				low = mid + 1;
		}

		return low;
	}

	public static int upper_bound(int[] arr, int x) {
		int low = 0, high = arr.length, mid = -1;

		while (low < high) {
			mid = (low + high) / 2;

			if (arr[mid] > x)
				high = mid;
			else
				low = mid + 1;
		}

		return low;
	}

	/////////////////////////////////////////////////////////////////////////////////////////////////////////

	static class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		FastScanner() throws FileNotFoundException {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		FastScanner(int a) throws FileNotFoundException {
			br = new BufferedReader(new FileReader("input.txt"));
		}

		String next() throws IOException {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			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());
		}

		String nextLine() throws IOException {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}

		int[] readArray(int n) throws IOException {
			int[] A = new int[n];
			for (int i = 0; i != n; i++) {
				A[i] = sc.nextInt();
			}
			return A;
		}

		long[] readArrayLong(int n) throws IOException {
			long[] A = new long[n];
			for (int i = 0; i != n; i++) {
				A[i] = sc.nextLong();
			}
			return A;
		}
	}

	static void ruffleSort(int[] a) {
		Random get = new Random();
		for (int i = 0; i < a.length; i++) {
			int r = get.nextInt(a.length);
			int temp = a[i];
			a[i] = a[r];
			a[r] = temp;
		}
		Arrays.sort(a);
	}

	static void ruffleSort(long[] a) {
		Random get = new Random();
		for (int i = 0; i < a.length; i++) {
			int r = get.nextInt(a.length);
			long temp = a[i];
			a[i] = a[r];
			a[r] = temp;
		}
		Arrays.sort(a);
	}
}