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 main() {
  unsigned long long i = 1, j = 1, n, k, c = 0;
  cin >> n >> k;
  cout << i << " " << i + k << " ";
  if (n == 1) {
    cout << 1;
    return 0;
  }
  while (1) {
    if (i + j < i + k - j)
      cout << i + j << " " << i + k - j << " ";
    else if (i + j == i + k - j) {
      cout << i + j << " ";
      break;
    } else
      break;
    c++;
    j++;
  }
  j = 2;
  while (k + j <= n && c < n) {
    cout << k + j << " ";
    j++;
  }
  return 0;
}
