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;
const long long inf = 0x7f7f7f7f;
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  ;
  long long n, k;
  cin >> n >> k;
  long long forw = 1;
  long long back = n;
  for (long long i = 0; i < k; i++) {
    if (i % 2)
      cout << back-- << " ";
    else
      cout << forw++ << " ";
  }
  if (k % 2)
    for (long long i = k; i < n; i++) cout << forw++ << " ";
  else
    for (long long i = k; i < n; i++) cout << back-- << " ";
  cout << endl;
  return 0;
}
