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 n, k, a, b;
signed main() {
  scanf("%d %d", &n, &k);
  a = 1;
  b = n;
  for (int i = 1; i <= n; i++) {
    if (i < k) {
      if (i & 1)
        cout << (a++) << " ";
      else
        cout << (b--) << " ";
    } else {
      if (i & 1)
        for (int j = a; j <= b; j++) cout << j << " ";
      else
        for (int j = b; j >= a; j--) cout << j << " ";
      return 0;
    }
  }
  return 0;
}
