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() {
  ios_base::sync_with_stdio(false);
  int n, k;
  while (cin >> n >> k) {
    int r = n, l = 1;
    cout << l;
    l++;
    for (int i = 1; i < k; i++)
      if (i % 2) {
        cout << " " << r;
        r--;
      } else {
        cout << " " << l;
        l++;
      }
    if (k % 2)
      for (int i = k; i < n; i++, l++) cout << " " << l;
    else
      for (int i = k; i < n; i++, r--) cout << " " << r;
    cout << endl;
  }
}
