Problem: Long story short, shashlik is Miroslav's favorite food. Shashlik is prepared on several skewers simultaneously. There are two states for each skewer: initial and turned over.

This time Miroslav laid out n skewers parallel to each other, and enumerated them with consecutive integers from 1 to n in order from left to right. For better cooking, he puts them quite close to each other, so when he turns skewer number i, it leads to turning k closest skewers from each side of the skewer i, that is, skewers number i - k, i - k + 1, ..., i - 1, i + 1, ..., i + k - 1, i + k (if they exist). 

For example, let n = 6 and k = 1. When Miroslav turns skewer number 3, then skewers with numbers 2, 3, and 4 will come up turned over. If after that he turns skewer number 1, then skewers number 1, 3, and 4 will be turned over, while skewer number 2 will be in the initial position (because it is turned again).

As we said before, the art of cooking requires perfect timing, so Miroslav wants to turn over all n skewers with the minimal possible number of actions. For example, for the above example n = 6 and k = 1, two turnings are sufficient: he can turn over skewers number 2 and 5.

Help Miroslav turn over all n skewers.

Input

The first line contains two integers n and k (1 ≤ n ≤ 1000, 0 ≤ k ≤ 1000) — the number of skewers and the number of skewers from each side that are turned in one step.

Output

The first line should contain integer l — the minimum number of actions needed by Miroslav to turn over all n skewers. After than print l integers from 1 to n denoting the number of the skewer that is to be turned over at the corresponding step.

Examples

Input

7 2


Output

2
1 6 


Input

5 1


Output

2
1 4 

Note

In the first example the first operation turns over skewers 1, 2 and 3, the second operation turns over skewers 4, 5, 6 and 7.

In the second example it is also correct to turn over skewers 2 and 5, but turning skewers 2 and 4, or 1 and 5 are incorrect solutions because the skewer 3 is in the initial state after these operations.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.lang.*;

public class cooking{
	
	public static void main(String[] args)
    {
		FastReader f = new FastReader();
		PrintWriter wr = new PrintWriter(System.out);
        int n,k;
        n = f.nextInt();
        k = f.nextInt();

        if(n==1 && k==0)
        {
            wr.println(1);
            wr.println(1);
            wr.close();
            return;
        }
        if(k>=n)
        {
            wr.println(1);
            wr.println(1);
            wr.close();
            return;
        }
        if((2*k+1)>=n && k<n )
        {
            wr.println(1);
            wr.println((n+1)/2);
            wr.close();
            return;
        }
        int x = n-(k+1);
        int y = 2*k + 1;
        if( x%y != 0 && x%y < (k+1))
        {
            int start = 1+k;
            ArrayList<Integer> ar = new ArrayList<Integer>();

            while(start<=n)
            {
                ar.add(start);
                start += 2*k +1;

            }

            wr.println(ar.size());
            for(Integer inn : ar)
            {
                wr.print(inn+" ");
            }
            wr.close();
            return;
        }
        int i = 1;
        ArrayList<Integer> array = new ArrayList<Integer>();


        while(i<=n)
        {
            array.add(i);
            i += 2*k + 1;
        }
        wr.println(array.size());
        for(Integer in : array)
        {
            wr.print(in+" ");
        }
        wr.close();
	}

	static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader()
        {
            br = new BufferedReader(new
                     InputStreamReader(System.in));
        }
 
        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;
        }
    }
}