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>
using namespace std;
int ans[100010], vis[100010];
int main() {
  int m, n, i, k, j;
  while (scanf("%d%d", &n, &k) != -1) {
    m = k;
    ans[1] = 1;
    memset(vis, 0, sizeof(vis));
    vis[1] = 1;
    for (i = 2; i <= k + 1; i++) {
      int tmp = ans[i - 1] + m;
      if (vis[tmp]) tmp = ans[i - 1] - m;
      if (tmp > k + 1) tmp = ans[i - 1] - m;
      ans[i] = tmp;
      vis[tmp] = 1;
      m--;
    }
    for (i = k + 2; i <= n; i++) ans[i] = i;
    for (i = 1; i <= n; i++) printf("%d ", ans[i]);
    printf("\n");
  }
  return 0;
}
