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;
ifstream input;
ofstream output;
int main(int argc, char *argv[]) {
  cin.sync_with_stdio(false);
  cout.sync_with_stdio(false);
  int len, rep;
  cin >> len >> rep;
  int tmp = len;
  int cur = 1;
  for (int i = 0; i < rep; i++) {
    if (i == 0)
      cur = 1;
    else {
      tmp--;
      if (i % 2 == 0)
        cur -= tmp;
      else
        cur += tmp;
    }
    cout << cur << " ";
  }
  if (rep % 2 == 0) {
    for (int j = rep; j < len; j++) {
      cur--;
      cout << cur << " ";
    }
  } else {
    for (int j = rep; j < len; j++) {
      cur++;
      cout << cur << " ";
    }
  }
  return 0;
}
