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 s, m;
  cin >> s >> m;
  for (int i = 1; i <= m / 2; ++i)
    cout << ((m % 2) ? i : s - i + 1) << " " << ((m % 2) ? s - i + 1 : i) << " "
         << '\n';
  for (int i = m / 2 + 1; i <= s - m / 2; ++i) cout << i << " " << '\n';
  cout << '\n';
  return 0;
}
