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 main() {
  int n, k, i;
  cin >> n >> k;
  if (k == 1) {
    for (i = 1; i <= n; i++) {
      cout << i << " ";
    }
    return 0;
  }
  int a[100002] = {0};
  int c = 1;
  int l = k;
  i = 1;
  while (c <= n) {
    if (c % 2 == 1) {
      printf("%d ", i);
      c++;
      a[i]++;
      if (c == l + 1) break;
    } else {
      printf("%d ", i + k);
      a[i + k]++;
      k -= 2;
      i++;
      c++;
      if (c == l + 1) {
        break;
      }
    }
  }
  for (i = 1; i <= n; i++) {
    if (!a[i]) cout << i << " ";
  }
  return 0;
}
