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 eps = 1e-8;
const int INF = 1000000000;
const int maxn = 100000 + 10;
int n, k;
int main() {
  scanf("%d%d", &n, &k);
  k++;
  int ss = k + 1;
  int index = 1, ji = 1, ou = k;
  while (k--) {
    if (index == 1) {
      index = 0;
      printf("%d ", ji++);
    } else {
      index = 1;
      printf("%d ", ou--);
    }
  }
  if (ss <= n) {
    for (int i = ss; i < n; i++) {
      printf("%d ", i);
    }
    printf("%d\n", n);
  }
  return 0;
}
