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;
long long int dict[1000001] = {0};
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  ;
  long long int n, k;
  cin >> n >> k;
  long long int start = 1;
  long long int end = n;
  long long int array[n - 1];
  long long int count = 0;
  bool toChange = true;
  while (k != 1) {
    if (toChange) {
      cout << start << " ";
      array[count] = start;
      count++;
      start++;
      toChange = false;
    } else {
      cout << end << " ";
      array[count] = end;
      count++;
      end--;
      toChange = true;
    }
    k--;
  }
  if (start <= end) {
    if (toChange) {
      for (long long int j = start; j <= end; j++) {
        array[count] = j;
        count++;
        cout << j << " ";
      }
    } else {
      for (long long int j = end; j >= start; j--) {
        array[count] = j;
        count++;
        cout << j << " ";
      }
    }
  }
  cout << endl;
  return 0;
}
