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 CPP):

Solution:
#include <bits/stdc++.h>
const long long LLINF = (1ll << 63) - 1;
const int INF = (1 << 31) - 1;
const long double PI = 3.141592653589793;
const long double EPS = 1e-15;
const int MOD = 1e9 + 7;
const int MOD2 = 16714589;
const int ENGLISH_ALPHABET_SIZE = 26;
const int N = 1e6 + 1;
const int M = 1e9 + 10;
using namespace std;
int main() {
  int n, k, start = 1;
  cin >> n >> k;
  vector<int> res;
  int div = n / (2 * k + 1), mod = n % (2 * k + 1);
  if (!mod) {
    for (int i = k + 1; i <= n; i += 2 * k + 1) res.push_back(i);
  } else if (div) {
    if (mod > k) {
      for (int i = k + 1; i < n - mod; i += 2 * k + 1) res.push_back(i);
      res.push_back(n - mod + k + 1);
    } else {
      res.push_back(1);
      div--;
      int i = 2 * k + 2;
      for (; div; i += 2 * k + 1, div--) res.push_back(i);
      res.push_back(i);
    }
  } else {
    res.push_back((n + 1) / 2);
  }
  cout << res.size() << endl;
  for (auto e : res) cout << e << " ";
  return 0;
}