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.*;
//Div 2
public class CF1040B {
   public static void main(String[] args) {
      Scanner sc = new Scanner(System.in);
      
      int n = sc.nextInt();
      int k = sc.nextInt();
      
      if(k==0)
        {
            System.out.println(n);
            for(int i=1;i<=n;i++)
            {
                System.out.print(i+" ");
            }
            System.out.println();
            return;
        }
        int ans=1000000000;
        ArrayList<Integer> a=new ArrayList<>();
        for(int i=1;i<=k+1;i++)
        {
            if(i>n)
                break;
            int st=i;
            int prev=0;
            ArrayList<Integer> ar=new ArrayList<>();
            while(st<=n)
            {
                ar.add(st);
                st+=(2*k+1);
            }
            if(ar.get(ar.size()-1)+k<n&&ar.get(ar.size()-1)+k==n-k-1)
                ar.add(n);
            if(ar.get(ar.size()-1)+k>=n)
            {
                if(ans>ar.size())
                {
                    ans=ar.size();
                    a=ar;
                }
            }
            
        }
        if(ans==1000000000)
            System.out.println(-1);
        else
        {
            System.out.println(ans);
            for(int i=0;i<ans;i++)
                System.out.print(a.get(i)+" ");
            System.out.println();
        }
   }
}