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.*;
public class F629{

	public static void main(String args[]){
		FastReader sc = new FastReader();
		StringBuilder sb=new StringBuilder();
        int t,i,n,k,j;
        long eq,op1,op2;
		t=1;
		while(t-->0){
            n=sc.nextInt();
            k=sc.nextInt();
            long a[]=new long[n];
            long pre[]=new long[n+1];
            long suff[]=new long[n+1];
            for(i=0;i<n;i++)
                a[i]=sc.nextLong();
            sort(a,0,n-1);
            for(i=0;i<n;i++)
                pre[i+1]=pre[i]+a[i];
            for(i=n-1;i>=0;i--)
                suff[i]=suff[i+1]+a[i];
            long min=Long.MAX_VALUE;
            for(i=0;i<n;){
                int count=0;
                for(j=i;j<n;j++){
                    if(a[j]==a[i])
                        count++;
                    else 
                        break;
                }
                if(count>=k){
                    min=0l;
                    //break;
                }
                if(count+i>=k){
                    eq=a[i]-1;
                    op1=Math.abs(eq*i-pre[i]);
                    min=Math.min(min,op1+k-count);
                }
                if(count+n-j>=k){
                    eq=a[i]+1;
                    op2=Math.abs(eq*(n-j)-suff[j]);
                    min=Math.min(min,op2+k-count);
                }
                op1=Math.abs((a[i]-1)*i-pre[i]);
                op2=Math.abs((a[i]+1)*(n-j)-suff[j]);
                min=Math.min(min,op1+op2+k-count);
                i=j;
            }
            sb.append(Math.max(min,0));
		}
		//sb.deleteCharAt(sb.length()-1);
		out.println(sb);
	}

	static PrintWriter out;
	static class FastReader{
		BufferedReader br;
		StringTokenizer st;
		public FastReader(){
			br=new BufferedReader(new InputStreamReader(System.in));
			out=new PrintWriter(System.out,true);
		}
		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());
		}
		String nextLine(){
			String str = "";
			try{
				str=br.readLine();
			}
			catch(IOException e){
				e.printStackTrace();
			}
			return str;
		}
	}

	public static boolean isPrime(int n) {
		if(n<2) return false;
		for(int i=2;i<=(int)Math.sqrt(n);i++) {
			if(n%i==0) return false;
		}
		return true;
	}

	public static void print(int a[],int l,int r){
		int i;
		for(i=l;i<=r;i++)
			out.print(a[i]+" ");
		out.println();
	}

	public static long fastexpo(long x, long y, long p){
		long res=1;
		while(y > 0){
			if((y & 1)==1)
				res= ((res%p)*(x%p))%p;
			y= y >> 1;			
			x = ((x%p)*(x%p))%p;
		}
		return res;
	}

	public static boolean[] sieve (int n) {
		boolean primes[]=new boolean[n+1];
		Arrays.fill(primes,true);
		primes[0]=primes[1]=false;
		for(int i=2;i*i<=n;i++){
			if(primes[i]){
				for(int j=i*i;j<=n;j+=i)
					primes[j]=false;
			}
		}
		return primes;
	}

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

    public static void merge(long a[],int l,int m,int r){
        int n1,n2,i,j,k;
        n1=m-l+1;
        n2=r-m;

        long L[]=new long[n1];
        long R[]=new long[n2];

        for(i=0;i<n1;i++)
            L[i]=a[l+i];
        for(j=0;j<n2;j++)
            R[j]=a[m+1+j];

        i=0;j=0;

        k=l;
        while(i<n1&&j<n2){
            if(L[i]<=R[j]){
                a[k]=L[i];
                i++;
            }
            else{
                a[k]=R[j];
                j++;
            }
            k++;
        }

        while(i<n1){
            a[k]=L[i];
            i++;
            k++;
        }
        while(j<n2){
            a[k]=R[j];
            j++;
            k++;
        }
    }
    public static void sort(long a[],int l,int r){
        int m;
        if(l<r){
            m=(l+r)/2;
            sort(a,l,m);
            sort(a,m+1,r);
            merge(a,l,m,r);
        }
    }
}