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>
int main() {
  int N, K;
  std::cin >> N >> K;
  for (int i = 1; i <= N; i = i + K + 1) {
    bool sign = true;
    int cur = i;
    if (cur <= N) {
      if (cur != 1) std::cout << " ";
      std::cout << cur;
    }
    for (int k = K; k >= 1; --k, sign = !sign) {
      cur = (sign ? cur + k : cur - k);
      if (cur <= N) std::cout << " " << cur;
    }
  }
  std::cout << std::endl;
  return 0;
}
