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, p1, p2, count;
  scanf("%d", &n);
  scanf("%d", &k);
  p1 = 1;
  p2 = 1 + k;
  count = 0;
  while (p2 - p1 > 0 && count < n) {
    printf("%d %d ", p1++, p2--);
    count += 2;
  }
  if (count < n) {
    if (p1 == p2) {
      printf("%d ", p1);
      count++;
      p1 = 2 + k;
    } else {
      p1 = 2 + k;
    }
    while (count < n) {
      printf("%d ", p1++);
      count++;
    }
  }
  return 0;
}
