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(0);
  cin.tie(0);
  cout.tie(0);
  long long n, k, vis[100001] = {0}, l = 1, r;
  cin >> n >> k;
  r = n;
  for (int i = 0; i < k; ++i) {
    if (!(i & 1)) {
      vis[l] = 1;
      cout << l++ << " ";
    } else {
      vis[r] = 1;
      cout << r-- << " ";
    }
  }
  if (k & 1)
    for (int i = 1; i <= n; ++i) {
      if (!vis[i]) {
        cout << i << " ";
      }
    }
  else
    for (int i = n; i > 0; --i) {
      if (!vis[i]) cout << i << " ";
    }
  cout << endl;
}
