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 = 0, k = 0, vis[100002];
  cin >> n >> k;
  memset(vis, false, sizeof(vis));
  int begin = 1, end = n;
  bool f = true;
  for (int i = 0; i < k; i++) {
    if (f) {
      cout << end << " ";
      end--, f = false;
    } else {
      cout << begin << " ";
      begin++, f = true;
    }
  }
  if (f) {
    for (int i = begin; i <= end; i++) {
      cout << i << " ";
    }
  } else {
    for (int i = end; i >= begin; i--) {
      cout << i << " ";
    }
  }
  return 0;
}
