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 int N = 1e6, oo = 1e9 + 7;
int main() {
  ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  long long int n, k, cnt = 1, trn;
  cin >> n >> k;
  trn = n;
  for (long long int i = 0; i < k; i++) {
    if (i % 2 == 0)
      cout << cnt++ << " ";
    else
      cout << trn-- << " ";
  }
  if (k % 2 == 0) {
    for (long long int i = trn; i >= cnt; i--) cout << i << " ";
  } else {
    for (long long int i = cnt; i <= trn; i++) cout << i << " ";
  }
  return (0);
}
