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 PYTHON3):

Solution:

# -*- coding: utf-8 -*-
#! @Date    : 2018-09-06 07:53:13
#! @Author  : raj lath (oorja.halt@gmail.com)
#! @Link    : "http://codeforces.com/contest/1040/problem/B"
#! @Version : 1.0.0

import os
from sys import stdin

max_val=int(10e12)
min_val=int(-10e12)

def read_int()     : return int(stdin.readline())
def read_ints()    : return [int(x) for x in stdin.readline().split()]
def read_str()     : return input()
def read_strs()    : return [x for x in stdin.readline()]
def read_str_list(): return [x for x in stdin.readline().split()]

nops, k = read_ints()
OFFSET = 2 * k + 1
rem  = nops % OFFSET
if nops < k+1:ans = [1]
elif rem <= k and rem != 0:
    ans = range(k + 1 - (k + 1-rem), nops+1, OFFSET)
else:
    ans = range(k + 1, nops + 1, OFFSET)
print(len(ans))
print(*ans)