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() {
  int n, k;
  cin >> n >> k;
  vector<int> cnt(n + 1, 0);
  vector<int> ans;
  ans.push_back(1);
  int foo = ans[(int)ans.size() - 1];
  cnt[foo] = 1;
  int tnd = 0;
  for (int i = k; i > 0; i--) {
    int temp;
    if (tnd % 2 == 0)
      temp = foo + i;
    else
      temp = foo - i;
    tnd++;
    tnd %= 2;
    if (cnt[temp] || temp < 1) continue;
    cnt[temp] = 1;
    ans.push_back(temp);
    foo = temp;
  }
  bool sp = false;
  for (int i = 0; i < (int)ans.size(); i++) {
    if (sp) cout << " ";
    cout << ans[i];
    sp = true;
  }
  for (int i = 1; i < (int)cnt.size(); i++) {
    if (cnt[i] == 0) {
      if (sp) cout << " ";
      cout << i;
      sp = true;
    }
  }
  cout << endl;
  return 0;
}
