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() {
  long long n, k, cont = 0, x = 1, ans = 0;
  bool foco = true;
  cin >> n >> k;
  long long re = n - k - 1;
  cout << x << " ";
  while (k--) {
    if (foco) {
      x = x + k + 1;
      ans = max(ans, x);
      foco = false;
    } else {
      x = x - k - 1;
      foco = true;
    }
    cout << x << " ";
    cont++;
  }
  x = ans;
  while (re--) {
    x += 1;
    cout << x << " ";
  }
  return 0;
}
