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 ar[100005] = {0}, n, x, k;
int main() {
  cin >> n >> k;
  int t = n - 1, p, tt = 1;
  cout << 1;
  ar[1] = 1;
  for (int i = 1; i <= n; i++) {
    if (k == 1) break;
    if (i % 2 == 1)
      tt = tt + t;
    else
      tt = tt - t;
    ar[tt] = 1;
    t--;
    cout << " " << tt;
    k--;
  }
  if (tt <= n / 2) {
    for (int i = 2; i <= n; i++)
      if (ar[i] == 0) cout << " " << i;
  } else {
    for (int i = tt - 1; i >= 2; i--)
      if (ar[i] == 0) cout << " " << i;
  }
  cout << endl;
}
