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() {
  long long int n, k;
  cin >> n >> k;
  int r[n + 1], x = 1;
  for (int i = 1; i <= n; i++) r[i] = x++, r[++i] = n - x + 2;
  for (int i = 1; i <= k; i++) cout << r[i] << " ";
  if (r[k] > n / 2)
    for (int i = k; i < n; i++) cout << --r[k] << " ";
  else
    for (int i = k; i < n; i++) cout << ++r[k] << " ";
  return 0;
}
