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() {
  int n, k;
  cin >> n >> k;
  if (k == 1)
    for (int i = 1; i <= n; ++i) cout << i << " ";
  else {
    int i = 1, j = n;
    int last = 0;
    while (k > 0) {
      cout << i << +" ";
      i++;
      k--;
      if (k == 0) {
        last = i;
        break;
      }
      cout << j << " ";
      j--;
      k--;
      if (k == 0) {
        last = j;
        break;
      }
    }
    if (last == i) {
      for (int l = i; l <= j; ++l) {
        cout << l << +" ";
      }
    } else {
      for (int l = j; l >= i; --l) {
        cout << l << +" ";
      }
    }
  }
  return 0;
}
