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, a, b, i, j;
  cin >> n >> k;
  a = 1;
  b = k + 1;
  while (b <= n) {
    b = min(a + k, n);
    for (i = a, j = b; i <= j; i++, j--) {
      if (i != j)
        cout << i << " " << j << " ";
      else
        cout << i << " ";
    }
    a = b + 1;
    if (b == n) break;
  }
  cout << "\n";
}
