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 n, k;
int bef;
int tmp;
int main() {
  int i;
  scanf("%d %d", &n, &k);
  if (1 + k < n)
    for (i = n; i > 1 + k; i--) printf("%d ", i);
  for (i = 0; i < 1 + k; i++)
    if (i % 2 == 0)
      printf("%d ", 1 + k - i / 2);
    else
      printf("%d ", 1 + i / 2);
  printf("\n");
  return 0;
}
