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, up, down;
  int ind = 1;
  cin >> n >> k;
  k++;
  up = n;
  down = 1;
  vector<int> ans;
  while (k != 1) {
    if (ind == 1)
      ans.push_back(up--);
    else
      ans.push_back(down++);
    ind *= -1;
    k--;
    n--;
  }
  if (ind == 1)
    while (n) {
      ans.push_back(down++);
      n--;
    }
  else
    while (n) {
      ans.push_back(up--);
      n--;
    }
  cout << ans[0];
  for (int i = 1; i < ans.size(); i++) cout << " " << ans[i];
}
