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:
import math
sashliks, spread = [int(i) for i in (input().split(' '))]
if sashliks <= spread*2+1:
    print('1\n' + str((sashliks//2)+1))
elif 2*spread+1 < sashliks and sashliks <= 2*(2*spread+1):
    if (sashliks - (2*(spread+1)) <= spread):
        print('2\n' + str(1 + sashliks - 2*(spread+1)) + ' ' + str(sashliks))
    else:
        print('2\n' + str(1+spread) + ' ' + str(2*spread+1+spread+1))
else:
    res = 0
    res = math.ceil((sashliks-2*(2*spread+1))/(2*spread+1))
    sashliks -= res*(2*spread+1)
    printres = ''
    if (sashliks - (2*(spread+1)) <= spread):
        printres += str(1+sashliks-2*(spread+1))
    else:
        printres += str(1+spread)
    last = int(printres)
    for i in range(res):
        printres += ' ' + str(last + 2*spread+1)
        last = last + 2*spread+1
    if (sashliks - (2*(spread+1)) <= spread):
        printres += ' ' + str(sashliks + res*(2*spread+1))
    else:
        printres += ' ' + str(2*spread+1+spread+1 + res*(2*spread+1))
    print(res + 2)
    print(printres)