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;
void print(int a[], int n) {
  for (int i = 0; i < n; i++) cout << a[i] << " ";
  cout << endl;
}
bool vis[100001] = {false};
int main() {
  int n, k;
  cin >> n >> k;
  vector<int> res;
  res.push_back(1);
  int l = 1;
  vis[1] = 1;
  for (int i = k; i > 0; i--) {
    if (l - i > 0 && !vis[l - i]) {
      res.push_back(l - i);
      vis[l - i] = 1;
      l = l - i;
    } else {
      res.push_back(l + i);
      vis[l + i] = 1;
      l = l + i;
    }
  }
  set<int> s;
  for (int i = 1; i < n + 1; i++)
    if (!vis[i]) s.insert(i);
  for (int i = 0; i < n - k - 1; i++) {
    set<int>::iterator it = s.lower_bound(l);
    if (it == s.end()) --it;
    res.push_back(*it);
    l = *it;
    s.erase(it);
  }
  for (int i = 0; i < res.size(); i++) cout << res[i] << " ";
  return 0;
}
