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 solve() {
  long long n, k;
  cin >> n >> k;
  long long d = 1;
  long long cur = 1;
  vector<int> ans;
  long long l = 1, r = k + 1;
  while (l < r) {
    ans.push_back(r--);
    if (l < r) ans.push_back(l++);
  }
  ans.push_back(l);
  k++;
  reverse(ans.begin(), ans.end());
  while (k < n) {
    ans.push_back(++k);
  }
  for (int i = n - 1; i >= 0; i--) {
    cout << ans[i] << ' ';
  }
  cout << endl;
}
int main() {
  int t = 1;
  while (t--) {
    solve();
  }
  return 0;
}
