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(0);
  cin.tie(0);
  int i, j, k, l, m, n;
  cin >> n >> k;
  if (k == 1) {
    for (i = 1; i <= n; i++) cout << i << " ";
    cout << endl;
  } else if (k == 2) {
    cout << "1 ";
    for (i = n; i > 1; i--) cout << i << " ";
    cout << endl;
  } else {
    l = 1;
    j = n;
    m = 1;
    while (k >= 2) {
      if (l % 2 == 0) {
        cout << j-- << " ";
      } else {
        cout << m++ << " ";
      }
      l++;
      k--;
    }
    if (l % 2)
      for (i = m; i <= j; i++) cout << i << " ";
    else
      for (i = j; i >= m; i--) cout << i << " ";
    cout << endl;
  }
  return 0;
}
