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:
//package CFSEP05;
import java.io.*;
import java.util.*;

public class Q2{

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader() {
            reader = new BufferedReader(new InputStreamReader(System.in), 32768);
            tokenizer = null;
        }

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(System.in), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public char nextChar() {
            return next().charAt(0);
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public int[] nextIntArr(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = this.nextInt();
            }
            return arr;
        }

        public Integer[] nextIntegerArr(int n) {
            Integer[] arr = new Integer[n];
            for (int i = 0; i < n; i++) {
                arr[i] = new Integer(this.nextInt());
            }
            return arr;
        }

        public int[][] next2DIntArr(int n, int m) {
            int[][] arr = new int[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    arr[i][j] = this.nextInt();
                }
            }
            return arr;
        }

        public int[] nextSortedIntArr(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = this.nextInt();
            }
            Arrays.sort(arr);
            return arr;
        }

        public long[] nextLongArr(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = this.nextLong();
            }
            return arr;
        }

        public char[] nextCharArr(int n) {
            char[] arr = new char[n];
            for (int i = 0; i < n; i++) {
                arr[i] = this.nextChar();
            }
            return arr;
        }
    }

    public static void main(String[] args) {

        InputReader in = new InputReader();
        int N = in.nextInt();
        int k=in.nextInt();
        long flag=0;
        ArrayList<Integer> frwd=new ArrayList<>();

        if(k==0){
            System.out.println(N);
            for(int i=1;i<=N;i++)
                System.out.print(i+ " ");
            return;
        }
        for (int i = 1; i <=N; ) {
            if(i!=1)
                i+=k+1;
            if(i>N)
                break;
            frwd.add(i);
            if(i>=N) {
                flag = 1;
                break;
            }
            i+=(k);
            if(i>=N) {
                flag = 1;
                break;
            }
        }


        if(flag==1) {
            System.out.println(frwd.size());
            for (int i = 0; i < frwd.size(); i++)
                System.out.print(frwd.get(i) + " ");
            return;
        }
        frwd.clear();

        for(int j=2;j<=k+1;j++) {
            for (int i = j; i <= N; ) {
                if (i != j)
                    i += k + 1;
                if(i>N)
                    break;
                frwd.add(i);
                if (i >= N) {
                    flag = 1;
                    break;
                }
                i += (k);
                if (i >= N) {
                    flag = 1;
                    break;
                }
            }
            if (flag == 1) {
                System.out.println(frwd.size());
                for (int i = 0; i < frwd.size(); i++)
                    System.out.print(frwd.get(i) + " ");
                return;
            }

            frwd.clear();
        }


    }
}