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(0);
  int n, k;
  cin >> n >> k;
  if (k == 1) {
    for (int i = 1; i <= n; i++) cout << i << " ";
    cout << "\n";
    return 0;
  }
  if (k == 2) {
    cout << "1 3 2 ";
    for (int i = 4; i <= n; i++) cout << i << " ";
    cout << "\n";
    return 0;
  }
  int z = k + 1;
  int l = 1, r = z;
  while (l <= r) {
    cout << l << " ";
    l++;
    if (l > r) break;
    cout << r << " ";
    r--;
  }
  for (int i = z + 1; i <= n; i++) cout << i << " ";
  cout << "\n";
  return 0;
}
