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;
  cin >> n >> k;
  int j = 1 + k;
  int i = 1;
  int l = 0;
  if (k == 1) {
    while (n > 0) cout << n-- << " ";
  } else {
    while (l <= k) {
      if (l % 2)
        cout << i++ << " ";
      else
        cout << j-- << " ";
      l++;
    }
    j = k + 2;
    while (j <= n) cout << j++ << " ";
  }
  return 0;
}
