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;
  cin >> n >> k;
  vector<int> ivv(n);
  int y = 1;
  int x = 0;
  bool b1 = false;
  for (int i = 0; i < n; i++) {
    if (k == 2) {
      b1 = true;
      k--;
      goto line1;
    } else if (k > 2) {
      if (i % 2 == 0) {
        ivv[i] = y;
        y++;
      } else {
        ivv[i] = n - x;
        x++;
        k -= 2;
      }
    } else {
    line1:
      ivv[i] = y;
      y++;
    }
  }
  if (b1 == true) {
    swap(ivv[n - 2], ivv[n - 1]);
  }
  for (int i = 0; i < n; i++) {
    cout << ivv[i] << " ";
  }
  return 0;
}
