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);
  int x = 1, y = n;
  while (k > 1) {
    if (k % 2 == 1) {
      printf("%d ", x);
      ++x;
    } else {
      printf("%d ", y);
      --y;
    }
    --k;
  }
  while (x <= y) {
    printf("%d%c", x, " \n"[x == y]);
    ++x;
  }
}
