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 int maxn = 1e5 + 5;
int n, k, p = 0;
bool t[maxn] = {0};
int main() {
  ios_base::sync_with_stdio(0);
  cin >> n >> k;
  int m = n;
  int l = n - k;
  for (int i = 0; i < n; i++) {
    t[m] = 1;
    cout << m << " ";
    m--;
    if (t[l] == 1) break;
    if (l == m)
      break;
    else {
      t[l] = 1;
      cout << l << " ";
      l++;
    }
    p++;
  }
  if (p < n) {
    for (int i = n - 1; i > 0; i--)
      if (t[i] == 0) cout << i << " ";
  }
  return 0;
}
