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;
const long long mod = 1e9;
long long n, k;
vector<bool> v(n + 1);
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> k;
  if (k == 1) {
    for (long long i = 1; i <= n; i++) cout << i << " ";
    return 0;
  }
  map<long long, bool> m;
  long long t = 1;
  cout << n << " ";
  m[n] = true;
  while (k) {
    if (t % 2) {
      cout << n - k << " ";
      m[n - k] = true;
      n -= k;
    } else {
      cout << n + k << " ";
      m[n + k] = true;
      n += k;
    }
    t++;
    k--;
  }
  for (long long i = n; i >= 1; i--) {
    if (!m[i]) cout << i << " ";
  }
  return 0;
}
