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 n, k, l = 1, r, c = 0;
  cin >> n >> k;
  r = n;
  while (1) {
    if (k - c <= 1) break;
    cout << l << " ";
    l++;
    c++;
    if (k - c != 1) {
      cout << r << " ";
      r--;
      c++;
    }
  }
  if (k % 2 == 0)
    for (int i = r; i >= l; i--) {
      cout << i << " ";
    }
  else {
    for (int i = l; i <= r; i++) {
      cout << i << " ";
    }
  }
  return 0;
}
