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::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n, k;
  cin >> n >> k;
  vector<int> v(n);
  vector<bool> used(n + 5);
  v[0] = used[1] = 1;
  bool inc = 1;
  int start = 1;
  for (int i = 1; k > 0; ++i) {
    int x = 0;
    if (inc)
      x = v[i - 1] + k;
    else
      x = v[i - 1] - k;
    v[i] = x;
    used[x] = true;
    inc = !inc;
    --k;
    start = i;
  }
  int x = 1;
  for (int i = start + 1; i < n; ++i) {
    while (used[x]) ++x;
    v[i] = x;
    used[x] = true;
  }
  for (int i = 0; i < n; ++i) {
    cout << v[i] << ' ';
  }
  cout << '\n';
  return 0;
}
