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;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n, k;
  cin >> n >> k;
  bool used[n];
  for (int i = 0; i <= n - 1; i++) used[i] = false;
  int a = 0, b = n - 1;
  for (int i = 0; i <= k - 1; i++) {
    if (i & 1)
      used[b] = true;
    else
      used[a] = true;
    if (i & 1)
      cout << (1 + (b--));
    else
      cout << (1 + (a++));
    cout << " ";
  }
  if (k & 1) {
    for (int i = 0; i <= n - 1; i++) {
      if (!used[i]) {
        cout << i + 1 << " ";
      }
    }
  } else {
    for (int i = n - 1; i >= 0; --i) {
      if (!used[i]) {
        cout << i + 1 << " ";
      }
    }
  }
  return 0;
}
