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 n, k;
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n >> k;
  int i = 2;
  int l = 1;
  cout << l << " ";
  bool up = true;
  int s = n - 1;
  while (i <= n) {
    i++;
    if (k == 1) {
      l += up ? 1 : -1;
      cout << l << " ";
      continue;
    }
    if (up)
      l += s;
    else
      l -= s;
    up = 1 - up;
    k--;
    s--;
    cout << l << " ";
  }
  cout << "\n";
}
