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, i;
  cin >> n >> k;
  for (i = 0; i != k; i++) {
    if (i % 2 == 0) {
      cout << i / 2 + 1 << " ";
    } else {
      cout << 1 + n - ((i - 1) / 2 + 1) << " ";
    }
  }
  if (k % 2 == 0) {
    for (i = (n - k / 2); (i >= k / 2 + 1); i--) {
      cout << i << " ";
    }
  } else {
    for (i = (k / 2 + 2); i <= (2 + n - (k / 2 + 2)); i++) {
      cout << i << " ";
    }
  }
  return 0;
}
