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() {
  int n, k;
  scanf("%d %d", &n, &k);
  set<int> s;
  set<int>::iterator it;
  for (int i = 1; i <= n - k; i++) {
    printf("%d ", i);
    s.insert(i);
  }
  printf("%d ", n);
  s.insert(n);
  int temp = n;
  for (int i = k - 1; i >= 1; i--) {
    it = s.find(temp - i);
    if (it == s.end() && (temp - i) > 0) {
      printf("%d ", temp - i);
      s.insert(temp - i);
      temp = temp - i;
    } else {
      printf("%d ", temp + i);
      s.insert(temp + i);
      temp = temp + i;
    }
  }
  return 0;
}
