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 argc, char const *argv[]) {
  int n, k, cnt = 1, p1, p2 = n + 1, f;
  cin >> n >> k;
  p2 = n + 1;
  for (int i = 1;; ++i) {
    cout << i << " ";
    p1 = i;
    cnt++;
    f = 1;
    if (cnt > k) break;
    cout << n - i + 1 << " ";
    p2 = n - i + 1;
    cnt++;
    f = 0;
    if (cnt > k) break;
  }
  if (f == 1) {
    for (int i = p1 + 1; i < p2; ++i) {
      cout << i << " ";
    }
  } else {
    for (int i = p2 - 1; i > p1; --i) {
      cout << i << " ";
    }
  }
  return 0;
}
