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() {
  std::ios::sync_with_stdio(false);
  int n, k, alt = 1, mini, maxi, cur;
  char last = '-';
  cin >> n >> k;
  cout << "1";
  cur = 1;
  maxi = n;
  n--;
  k--;
  mini = 2;
  while (n--) {
    if (alt && k) {
      cout << " " << maxi;
      cur = maxi;
      maxi--;
      alt = 0;
      k--;
      last = '+';
    } else if (k) {
      cout << " " << mini;
      cur = mini;
      mini++;
      alt = 1;
      k--;
      last = '-';
    } else {
      if (last == '+') {
        cur--;
        cout << " " << cur;
      } else {
        cur++;
        cout << " " << cur;
      }
    }
  }
  cout << endl;
}
