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 n, k;
bool is[100001], fs;
vector<int> ans;
int main() {
  scanf("%d%d", &n, &k);
  ans.push_back(1);
  is[1] = true;
  for (int i = 1, j = 1; j < k; ++j) {
    if (fs) {
      ans.push_back(++i);
      is[i] = true;
      fs = false;
      continue;
    }
    ans.push_back(k - i + 2);
    is[k - i + 2] = true;
    fs = true;
  }
  for (int i = (0); i < (ans.size()); ++i) printf("%d ", ans[i]);
  for (int i = (1); i < (n + 1); ++i)
    if (is[i] == false) printf("%d ", i);
  return 0;
}
