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> v;
  for (int i = 0; i < n - k + 1; i++) v.push_back(i);
  int mi = 0, ma = v.back();
  for (int i = n - k + 1, j = 0; i < n; i++, j++) {
    if (j % 2) {
      ++ma;
      v.push_back(ma);
    } else {
      --mi;
      v.push_back(mi);
    }
  }
  for (int i = 0; i < (int)(n); ++i) v[i] -= mi - 1;
  for (int i = 0; i < (int)(v.size()); ++i) {
    if (i > 0) printf(" ");
    printf("%d", v[i]);
  }
  printf("\n");
  return 0;
}
