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() {
  ios_base::sync_with_stdio(false);
  long long i, n, k, m = 0, z, qqqq;
  cin >> n >> k;
  long long arr[n];
  qqqq = k + 1;
  for (i = 1;; i++) {
    arr[m++] = i;
    if (m == k) break;
    arr[m++] = qqqq--;
    if (m == k) break;
  }
  qqqq++;
  for (z = i + 1; z <= n; z++) {
    if ((z < qqqq) || (z > k + 1)) arr[m++] = z;
  }
  for (i = 0; i <= n - 1; i++) cout << arr[i] << " ";
  ;
  return 0;
}
