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 a[100005];
int main() {
  int n, k;
  scanf("%d %d", &n, &k);
  int i = k + 1, j = 1, idx = k + 1;
  while (idx > 0) {
    a[idx] = i--, a[idx - 1] = j++;
    idx -= 2;
  }
  for (int i = k + 2; i <= n; i++) a[i] = i;
  for (int i = 1; i <= n; i++) printf("%d ", a[i]);
  printf("\n");
  return 0;
}
