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>
using namespace std;
long long int turned[1007];
long long int n, k;
vector<long long int> vs, ansv;
long long int recur(long long int num, long long int x) {
  if (num > n) return INT_MAX;
  vs.push_back(num);
  if (num >= n) return 1;
  return 1 + recur(num + 2 * k + 1, x + 1);
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int i, j, u, v, maxturn, ans = INT_MAX;
  cin >> n >> k;
  u = n / 2;
  if (n - k <= 0) {
    cout << 1 << '\n' << 1 << '\n';
    return 0;
  }
  if (2 * k + 1 >= n) {
    u = n / 2 + 1;
    cout << 1 << '\n' << u << '\n';
    return 0;
  }
  for (i = 1; i <= 1007; i++) ansv.push_back(i);
  for (i = 1; i <= k + 1; i++) {
    vs.clear();
    vs.push_back(i);
    j = i + 2 * k + 1;
    while (1) {
      if (j > n) {
        vs.clear();
        break;
      } else {
        if (j >= n - k) {
          vs.push_back(j);
          if (vs.size() < ansv.size()) ansv = vs;
          break;
        } else {
          vs.push_back(j);
          j = j + 2 * k + 1;
        }
      }
    }
  }
  cout << ansv.size() << '\n';
  for (i = 0; i < ansv.size(); i++) cout << ansv[i] << " ";
  cout << '\n';
  return 0;
}