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;
  bool taken[200000] = {false};
  cin >> n >> k;
  int x = 1;
  cout << x << ' ';
  taken[1] = true;
  for (int j = 0, i = k; j < n - 1 && i; j++, i--) {
    if (x - i > 0 && !taken[x - i])
      taken[x - i] = true, x -= i, cout << x << ' ';
    else if (x + i <= n && !taken[x + i])
      taken[x + i] = true, x += i, cout << x << ' ';
  }
  for (int i = 1; i <= n; i++)
    if (!taken[i]) cout << i << ' ';
  return 0;
}
