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() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int k, n;
  cin >> n >> k;
  int r = k + 1, l = 1;
  vector<int> t(n + 1, 0);
  while (l < r) {
    cout << l << " " << r << " ";
    t[r] = t[l] = 1;
    l++;
    r--;
  }
  for (int i = 1; i <= n; ++i)
    if (!t[i]) cout << i << " ";
  cout << '\n';
  return 0;
}
