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;
long long fact(long long k) {
  if (k == 0) return 1;
  return k * fact(k - 1);
}
signed main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  long long n, k, j = 0;
  cin >> n >> k;
  long long a[n], b[k];
  for (long long i = 1; i <= n; i++) {
    a[i - 1] = i;
    if (i >= 2 && i <= k + 1) {
      b[j] = i;
      j++;
    }
  }
  if (k == 1) {
    for (auto x : a) cout << x << " ";
  } else {
    long long start = 0;
    long long end = k - 1;
    cout << "1"
         << " ";
    while (start <= end) {
      cout << b[end] << " ";
      if (start < end) cout << b[start] << " ";
      start++;
      end--;
    }
    if (n > k + 1) {
      for (long long i = k + 1; i < n; i++) cout << a[i] << " ";
    }
  }
}
