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(NULL);
  int n, k;
  cin >> n >> k;
  cout << 1 << " ";
  int l = k;
  int a = 1;
  bool cnt[n + 1];
  memset(cnt, false, n + 1);
  cnt[1] = true;
  for (int i = 0; i < k; i++) {
    if (i % 2 == 0)
      a += l;
    else
      a -= l;
    cnt[a] = true;
    l--;
    cout << a << " ";
  }
  for (int i = 1; i <= n; i++) {
    if (cnt[i] == false) cout << i << " ";
  }
  return 0;
}
