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 v[100005] = {0};
  int n, k;
  cin >> n >> k;
  cout << "1 ";
  int i = 1;
  v[1] = 1;
  bool ok = true;
  while (k) {
    if (ok) {
      cout << i + k << " ", v[i + k] = 1, i = i + k;
    } else {
      cout << i - k << " ", v[i - k] = 1, i -= k;
    }
    k--;
    ok = !ok;
  }
  for (int j = 2; j <= n; j++) {
    if (!v[j]) cout << j << " ";
  }
  return 0;
}
