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;
const int maxn = 1e5 + 5;
int n, k;
int a[maxn];
int main() {
  while (~scanf("%d%d", &n, &k)) {
    for (int i = 1; i <= n; i++) a[i] = i;
    if (k == 1)
      for (int i = 1; i <= n; i++) printf("%d%c", a[i], i == n ? '\n' : ' ');
    else {
      a[1] = 1;
      int f = 1;
      int i;
      for (i = 2; i <= n && k; i++) {
        if (f > 0) {
          a[i] = a[i - 1] + k;
          k--;
        } else {
          a[i] = a[i - 1] - k;
          k--;
        }
        f = -f;
      }
      for (int i = 1; i <= n; i++) printf("%d%c", a[i], i == n ? '\n' : ' ');
    }
  }
  return 0;
}
