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 n, k, a[100005];
int main() {
  cin >> n >> k;
  int ed = 0;
  for (int i = 1, j = k + 1; i <= j; i++, j--) {
    a[(i - 1) * 2 + 1] = i;
    ed = (i - 1) * 2 + 1;
    if (j > i) {
      a[(i - 1) * 2 + 2] = j;
      ed = (i - 1) * 2 + 2;
    } else
      break;
  }
  for (int i = ed + 1; i <= n; i++) a[i] = i;
  for (int i = 1; i <= n; i++) {
    printf("%d ", a[i]);
  }
  puts("");
  return 0;
}
