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);
  if (k == 1) {
    for (int i = 1; i <= n; i++) {
      if (i - 1) printf(" ");
      printf("%d", i);
    }
    return 0;
  }
  vector<int> v;
  int a = 1, b = n;
  for (int i = 0; i < n; i++)
    if (i & 1)
      v.push_back(b--);
    else
      v.push_back(a++);
  sort(v.begin() + k, v.end());
  if (!(k & 1)) reverse(v.begin() + k, v.end());
  for (int i = 0; i < n; i++) {
    if (i) printf(" ");
    printf("%d", v[i]);
  }
}
