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;
template <typename T, typename T2>
ostream &operator<<(ostream &s, const pair<T, T2> &p) {
  return s << "(" << p.first << "," << p.second << ")";
}
template <typename T, typename T2>
istream &operator>>(istream &s, const pair<T, T2> &p) {
  return s >> p.first >> p.second;
}
template <typename T>
ostream &operator<<(ostream &s, const vector<T> &v) {
  for (auto it : v) s << it << " ";
  return s;
}
template <typename T>
void read_input(T beg, T end) {
  while (beg != end) cin >> *beg++;
}
struct debugger {
  template <typename T>
  debugger &operator,(const T &v) {
    cerr << v << ", ";
    return *this;
  }
} dbg;
int main() {
  ios_base::sync_with_stdio(false);
  int n, m;
  cin >> n >> m;
  bool add = true;
  int last = 1;
  cout << last << " ";
  for (int i = m; i >= 1; i--) {
    if (add) {
      last += i;
      add = false;
    } else {
      last -= i;
      add = true;
    }
    cout << last << " ";
  }
  for (int i = 2 + m; i <= n; i++) cout << i << " ";
  return 0;
}
