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.io.*;
import java.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.regex.*;

public class Solution {
    public static void main(String[] args)throws IOException {
        BufferedReader bf= new BufferedReader(new InputStreamReader(System.in));
        String[] s= bf.readLine().trim().split("\\s+");
        int n= Integer.parseInt(s[0]);
        int k= Integer.parseInt(s[1]);
        int bstart= k+1;
        ArrayList<Integer> ans= new ArrayList<>();
        ans.add(bstart);
        int end=2*k+1;
        while(end<=n){
            if(end==n)
                break;
            bstart=bstart+2*k+1;
            end=end+2*k+1;
//            if(end<=n)
                ans.add(bstart);
        }
        while(!(ans.get(ans.size()-1)<=n)){
            for(int i=0;i<ans.size();i++){
                ans.set(i,ans.get(i)-1);
            }
        }
        ArrayList<Integer> q= new ArrayList<>();
        for(int i=0;i<ans.size();i++){
            if(ans.get(i)>0) {
                q.add(ans.get(i));
            }
        }
        System.out.println(q.size());
        for(int i=0;i<q.size();i++)
            System.out.print(q.get(i)+" ");
//        System.out.println();
    }
}