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;
signed main() {
  long long n, k;
  cin >> n >> k;
  long long s = 1;
  long long e = k + 1;
  for (long long i = 1; i <= k + 1; i++) {
    if (i % 2 == 1) {
      cout << s << " ";
      s++;
    } else {
      cout << e << " ";
      e--;
    }
  }
  s = k + 2;
  for (long long i = k + 2; i <= n; i++) {
    cout << s << " ";
    s++;
  }
}
