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;
bool vis[100006];
int main() {
  int n, k;
  while (cin >> n >> k) {
    memset(vis, false, sizeof(vis));
    int st = 1, ed = 1 + k;
    int cnt = 0;
    while (cnt < k && st <= ed) {
      if (st != ed)
        vis[st] = vis[ed] = true, cout << st << ' ' << ed << ' ';
      else
        vis[st] = true, cout << st << ' ';
      st++, ed--;
      cnt++;
    }
    for (int i = 1; i <= n; i++) {
      if (!vis[i]) cout << i << ' ';
    }
    puts("");
  }
  return 0;
}
