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;
const int N = 1e5 + 9;
int k, n, i, j, p, v, a[N];
int main() {
  scanf("%d%d", &n, &k);
  for (i = 1; i <= n; i++) a[i] = i;
  for (i = 1; i <= n - k; i++) {
    p = a[i] = i;
  }
  v = k;
  for (; i <= n; i++) {
    if (j % 2 == 0) {
      p = a[i] = p + v;
    } else {
      p = a[i] = p - v;
    }
    j++;
    v--;
  }
  for (i = 1; i <= n; i++) printf("%d ", a[i]);
  return 0;
}
