B. Shashlik Cooking

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本文介绍了一个关于烧烤串翻转的算法问题，通过分析如何以最少的步骤翻转所有烧烤串，提供了一种有效的解决方案。对于n个并排的烧烤串，每次操作可以翻转目标串及其两侧k个串的状态，文章给出了确定最小操作次数及具体操作序列的方法。

题目链接：http://codeforces.com/contest/1040/problem/B

B. Shashlik Cooking

time limit per test

1 second

memory limit per test

512 megabytes

input

standard input

output

standard output

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 nn skewers parallel to each other, and enumerated them with consecutive integers from 11 to nn in order from left to right. For better cooking, he puts them quite close to each other, so when he turns skewer number ii, it leads to turning kk closest skewers from each side of the skewer ii, that is, skewers number i−ki−k, i−k+1i−k+1, ..., i−1i−1, i+1i+1, ..., i+k−1i+k−1, i+ki+k (if they exist).

For example, let n=6n=6 and k=1k=1. When Miroslav turns skewer number 33, then skewers with numbers 22, 33, and 44 will come up turned over. If after that he turns skewer number 11, then skewers number 11, 33, and 44 will be turned over, while skewer number 22 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 nn skewers with the minimal possible number of actions. For example, for the above example n=6n=6 and k=1k=1, two turnings are sufficient: he can turn over skewers number 22 and 55.

Help Miroslav turn over all nn skewers.

Input

The first line contains two integers nn and kk (1≤n≤10001≤n≤1000, 0≤k≤10000≤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 ll — the minimum number of actions needed by Miroslav to turn over all nn skewers. After than print llintegers from 11 to nn denoting the number of the skewer that is to be turned over at the corresponding step.

Examples

input

Copy

7 2

output

Copy

2
1 6

input

Copy

5 1

output

Copy

2
1 4

Note

In the first example the first operation turns over skewers 11, 22 and 33, the second operation turns over skewers 44, 55, 66 and 77.

In the second example it is also correct to turn over skewers 22 and 55, but turning skewers 22 and 44, or 11 and 55 are incorrect solutions because the skewer 33 is in the initial state after these operations.

#include<iostream>
using namespace std;
int main()
{
	int n,k,d,i,q,r;
	cin>>n>>k;
	d=2*k+1;
	q=n/d;
	r=n%d;
	if(r!=0)
		q++;
	else
		r=2*k;
	cout<<q<<endl;
	for(i=1+r/2;i<=n;i+=d)
		cout<<i<<" ";
	return 0;
}