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 a[100010];
int main() {
  int n, k, i;
  while (scanf("%d%d", &n, &k) == 2) {
    k -= 1;
    if (k % 2 == 0) {
      for (i = 1; i <= k + 1; i += 2) a[i] = (i + 1) / 2;
      for (i = 2; i <= k; i += 2) a[i] = n - a[i - 1] + 1;
      for (i = k + 2; i <= n; i++) a[i] = a[i - 1] + 1;
    } else {
      for (i = 1; i <= k; i += 2) a[i] = (i + 1) / 2;
      for (i = 2; i <= k + 1; i += 2) a[i] = n - a[i - 1] + 1;
      for (i = k + 2; i <= n; i++) a[i] = a[i - 1] - 1;
    }
    for (i = 1; i < n; i++) printf("%d ", a[i]);
    printf("%d\n", a[n]);
  }
  return 0;
}
