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;
const double PI = acos(-1.0);
int n, k, a[1000 * 1000], w[1000 * 1000], was[1000 * 1000];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cin >> n >> k;
  for (int i = 1; i <= n - k; i++) cout << i << " ";
  int c = 1;
  int p1 = n - k + 1;
  int p2 = n;
  for (int i = n - k + 1; i <= n; i++) {
    if (c & 1) {
      cout << p2 << " ";
      p2--;
    } else {
      cout << p1 << " ";
      p1++;
    }
    c++;
  }
  return 0;
}
