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;
set<int> s;
set<int> t;
int n, k;
void input();
void solve();
int main() {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  input();
  solve();
  return 0;
}
void input() {
  cin >> n >> k;
  for (int i = 1; i <= n; i++) s.insert(i);
}
void solve() {
  for (int i = 0; i < k; i++) {
    if (i % 2 == 0) {
      cout << *s.begin() << " ";
      s.erase(s.begin());
    } else {
      cout << *s.rbegin() << " ";
      s.erase(*s.rbegin());
    }
  }
  if (k % 2 == 0) {
    for (auto i : s) t.insert(-i);
    for (auto i : t) cout << -i << " ";
    return;
  }
  for (auto i : s) cout << i << " ";
}
