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 sept;

import java.io.*;
import java.util.*;

public class Rnd507 {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
    //boolean codechef=true;
    boolean codechef=true;
    
	void solve()
	{
		int n=ni(),k=ni();
		ArrayList<Integer> ans=new ArrayList<>();
		ans.add(Math.min(n, k+1));
		int lastFill=ans.get(ans.size()-1)+k;
		for(int i=k+1+2*k+1;i<=n;i+=2*k+1)
		{
			ans.add(i);
		    lastFill=ans.get(ans.size()-1)+k;
		}
		if(lastFill<n)
		{
			//ans.add(n);
			int tmp=lastFill;
			int rem=n-(tmp+1)+1;
			int req=(k+1)-rem;
			int sz=ans.size();
			for(int i=0;i<sz;i++)
			{
				ans.set(i, ans.get(i)-req);
			}
			ans.add(n);
		}
		out.println(ans.size());
		for(int i:ans)
		{
			out.print(i+" ");
		}
		out.println();
	}
	
	static int[][] packD(int n, int[] from, int[] to) {
		int[][] g = new int[n][];
		int[] p = new int[n];
		for (int f : from)
			p[f]++;
		for (int i = 0; i < n; i++)
			g[i] = new int[p[i]];
		for (int i = 0; i < from.length; i++) {
			g[from[i]][--p[from[i]]] = to[i];
		}
		return g;
	}
    
    public boolean check(int[] cnt,int m)
    {
    	boolean ch=true;
    	for(int i=2;i<=m;i++)
		{
			if(cnt[i]>=cnt[1])
			{
				ch=false;break;
			}
		}
		return ch;
    }
    
    static long[] dp;
    
    public long comp(Pair[] arr,int st,int end,int [] cnt,int m)
    {
    	boolean ch=check(cnt,m);
    	//System.out.println("st:"+st);
    	//System.out.println(Arrays.toString(cnt));
    	if(ch)
    	{
    		//System.out.println(st+" "+Arrays.toString(cnt));
    		return 0;
    	}
    	if(st==end)
    	{
    		cnt[arr[st].a]--;
    		cnt[1]++;
    		ch=check(cnt,m);
    		if(ch)
    		{
    			cnt[arr[st].a]++;
        		cnt[1]--;
    			return arr[st].b;
    		}
    		else
    		{
    			cnt[arr[st].a]++;
        		cnt[1]--;
        		return Long.MAX_VALUE;
    		}
    	}
    	//if(dp[st]!=-1)return dp[st];
    	
    	long min=comp(arr,st+1,end,cnt,m);
    	cnt[arr[st].a]--;
    	cnt[1]++;
    	long val=comp(arr,st+1,end,cnt,m);
    	if(val==Long.MAX_VALUE)val=Long.MAX_VALUE-arr[st].b;
    	min=Math.min(min,arr[st].b+val);
    	cnt[arr[st].a]++;
    	cnt[1]--;
    	dp[st]=min;
    	//System.out.println(min);
    	return min;
    }
    
    static class Temp
    {
    	int diff;
    	int id1;int id2;
    	int a2b;
    	public Temp(int diff,int id1,int id2,int a2b)
    	{
    		this.diff=diff;
    		this.id1=id1;
    		this.id2=id2;
    		this.a2b=a2b;
    	}
    }
	    
    static class Pair
    {
        int a,b;
        public Pair(int a,int b)
        {
            this.a=a;
            this.b=b;
        }
    }
    
    static long lcm(int a,int b)
    {
        long val=a;
        val*=b;
        return (val/gcd(a,b));
    }
    
    static int gcd(int a,int b)
    {
        if(a==0)return b;
        return gcd(b%a,a);
    }
    
    static int pow(int a, int b, int p)
    {
        long ans = 1, base = a;
        while (b!=0)
        {
            if ((b & 1)!=0)
            {
                ans *= base;
                ans%= p;
            }
            base *= base;
            base%= p;
            b >>= 1;
        }
        return (int)ans;
    }

    static int inv(int x, int p)
    {
        return pow(x, p - 2, p);
    }

    
    void run() throws Exception
    {
        if(codechef)oj=true;
        is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        
        long s = System.currentTimeMillis();
        solve();
        out.flush();
        tr(System.currentTimeMillis()-s+"ms");
    }
    
    public static void main(String[] args) throws Exception {new Rnd507().run();}
    
    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;
    
    private int readByte()
    {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }
    
    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    
    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }
    
    private String ns()
    {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    private char[] ns(int n)
    {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    private char[][] nm(int n, int m)
    {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }
    
    private int[] na(int n)
    {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }
    
    private int ni()
    {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private long nl()
    {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
    private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}