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>
int main() {
  int n, k, i;
  scanf("%d%d", &n, &k);
  for (i = 1; i <= n - k; i++) {
    printf("%d ", i);
  }
  int j = n;
  i = n - k + 1;
  if (i == n) {
    printf("%d", j);
    return 0;
  }
  while (i < j) {
    printf("%d %d ", j, i);
    j = j - 1;
    i = i + 1;
  }
  if (i == j) {
    printf("%d", i);
  }
  return 0;
}
