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, x, i = 0, l, r;
  cin >> n >> x;
  for (i = 1; i <= n - x; i++) printf("%d ", i);
  r = n;
  l = n - x + 1;
  for (i = 1; i <= x; i++) {
    if (i % 2)
      printf("%d ", r), r--;
    else
      printf("%d ", l), l++;
  }
  return 0;
}
