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>
int n, k;
int a[110000];
int main() {
  scanf("%d%d", &n, &k);
  int min, max;
  min = 1;
  max = n;
  if (k == 1) {
    for (int i = 1; i <= n; ++i) printf("%d ", i);
    return 0;
  }
  for (int i = 0; i < k; ++i) {
    if (i % 2) {
      a[i] = min;
      ++min;
    } else {
      a[i] = max;
      --max;
    }
  }
  if (k % 2)
    for (int i = k; i < n; ++i) {
      a[i] = max;
      --max;
    }
  else
    for (int i = k; i < n; ++i) {
      a[i] = min;
      ++min;
    }
  for (int i = 0; i < n; ++i) printf("%d ", a[i]);
}
