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 N = 1e6 + 9;
long long n, k;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cerr << "‌";
  cin >> n >> k;
  for (long long i = n; i > 1 + k; i--) cout << i << ' ';
  long long cur = 1 + k;
  for (int i = 0; i < ((k + 1) / 2); i++) {
    cout << cur << ' ' << 2 + k - cur << ' ';
    cur--;
  }
  if ((k + 1) & 1) cout << (k + 1) / 2 + 1;
}
