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, l, r;
  bool f = false;
  scanf("%d %d", &n, &k);
  l = 1;
  r = n;
  for (int i = 0; i < k; i++) {
    if (!f) {
      printf("%d ", r--);
      f = !f;
    } else {
      printf("%d ", l++);
      f = !f;
    }
  }
  if (f) {
    for (int i = r; i >= l; i--) {
      printf("%d", i);
      if (i == l)
        printf("\n");
      else
        printf(" ");
    }
  } else {
    for (int i = l; i <= r; i++) {
      printf("%d", i);
      if (i == r)
        printf("\n");
      else
        printf(" ");
    }
  }
  return 0;
}
