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;
  scanf("%d", &n);
  ;
  scanf("%d", &k);
  ;
  int x;
  vector<int> res;
  map<int, bool> mark;
  res.emplace_back(1);
  mark[1] = 1;
  int prev = 1;
  int kk = k;
  for (x = kk; x >= 1; x--) {
    if (prev - k <= n && prev - k > 0 && !mark[prev - k])
      res.emplace_back(prev - k), mark[prev - k] = 1, prev = prev - k;
    else if (prev + k <= n && !mark[prev + k])
      res.emplace_back(prev + k), mark[prev + k] = 1, prev = prev + k;
    k--;
  }
  for (auto it : res) printf("%d ", it);
  for (x = 1; x <= n; x++)
    if (!mark[x]) printf("%d ", x);
}
