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;
int n, k, t[100005];
int main() {
  int p, i, x;
  cin >> n >> k;
  p = k + 1;
  x = p;
  for (i = p; i >= 1; i -= 2) {
    t[i] = x;
    --x;
  }
  if (i == 0)
    for (i = 1; i <= p; i += 2) {
      t[i] = x;
      x--;
    }
  else
    for (i = 2; i <= p; i += 2) {
      t[i] = x;
      x--;
    }
  for (i = p + 1; i <= n; ++i) t[i] = i;
  for (i = 1; i <= n; ++i) cout << t[i] << " ";
  cout << "\n";
  return 0;
}
