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, j = 1;
  bool minus = false;
  cin >> n >> k;
  cout << "1 ";
  n--;
  i = k;
  while (n--) {
    if (i > 0) {
      if (minus) {
        j -= i;
        minus = false;
      } else {
        j += i;
        minus = true;
      }
      i--;
    } else if (i == 0) {
      j = k + 2;
      i--;
    } else
      j++;
    cout << j << ' ';
  }
  return 0;
}
