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 n2, k2, i;
  scanf("%d%d", &n2, &k2);
  if (k2 == 1) {
    for (i = 1; i < n2; i++) printf("%d ", i);
    printf("%d\n", n2);
  } else {
    if (k2 == n2 - 1) {
      for (i = 1; i <= n2 / 2; i++) printf("%d %d ", n2 - i + 1, i);
      if (n2 % 2 == 1)
        printf("%d\n", n2 / 2 + 1);
      else
        printf("\n");
    } else {
      int l = 0, u, j = 0, t = 0, f = 0;
      while (1) {
        printf("%d ", n2 - l);
        j++;
        f++;
        if (j == k2) break;
        printf("%d ", l + 1);
        j++;
        t++;
        if (j == k2) break;
        l++;
      }
      if (f > t) {
        j = 1 + t;
        printf("%d", n2 - f);
        for (i = n2 - f - 1; i >= j; i--) printf(" %d", i);
        printf("\n");
      } else {
        j = 1 + t;
        printf("%d", j);
        for (i = j + 1; i <= n2 - f; i++) printf(" %d", i);
        printf("\n");
      }
    }
  }
}
