Permutation p is an ordered set of integers p1, p2, ..., pn, consisting of n distinct positive integers not larger than n. We'll denote as n the length of permutation p1, p2, ..., pn.

Your task is to find such permutation p of length n, that the group of numbers |p1 - p2|, |p2 - p3|, ..., |pn - 1 - pn| has exactly k distinct elements.

Input

The single line of the input contains two space-separated positive integers n, k (1 ≤ k < n ≤ 105).

Output

Print n integers forming the permutation. If there are multiple answers, print any of them.

Examples

Input

3 2


Output

1 3 2


Input

3 1


Output

1 2 3


Input

5 2


Output

1 3 2 4 5

Note

By |x| we denote the absolute value of number x. 
#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long n, k, pr, i;
  cin >> n >> k;
  long long vis[100005] = {0};
  vector<long long> v;
  v.push_back(1);
  vis[1] = 1;
  pr = 1;
  while (k) {
    if (pr - k >= 1 && !vis[pr - k])
      v.push_back(pr - k), vis[pr - k] = 1, pr -= k;
    else if (pr + k <= n && !vis[pr + k])
      v.push_back(pr + k), vis[pr + k] = 1, pr += k;
    k--;
  }
  long long sz = v.size();
  for (i = 0; i < sz; i++) cout << v[i] << " ";
  for (i = 1; i <= n; i++)
    if (!vis[i]) cout << i << " ";
  return 0;
}
