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() {
  int n = 0, a[100004] = {0}, vis[100005] = {0}, t = 0, k = 0, m = 0, i = 0,
      j = 0, ans = 0;
  string str, s;
  vector<pair<int, int> > v;
  cin >> n >> k;
  a[0] = 1;
  vis[1] = 1;
  cout << 1 << " ";
  for (i = 1; i < n; i++) {
    if (i % 2) {
      cout << k + a[i - 1] << " ";
      vis[k + a[i - 1]] = 1;
      a[i] = k + a[i - 1];
    } else {
      cout << a[i - 1] - k << " ";
      vis[a[i - 1] - k] = 1;
      a[i] = a[i - 1] - k;
    }
    k--;
    if (k == 0) {
      i++;
      break;
    }
  }
  for (i = 1; i <= n; i++)
    if (vis[i] == 0) cout << i << " ";
  return 0;
}
