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;
int main(void) {
  scanf("%d%d", &N, &K);
  int l = 0, h = N + 1;
  for (int i = 0; i < K; ++i) {
    if (i & 1)
      printf("%d ", --h);
    else
      printf("%d ", ++l);
  }
  if (K & 1)
    for (int i = l + 1; i < h; ++i) printf("%d ", i);
  else
    for (int i = h - 1; i > l; --i) printf("%d ", i);
  return 0;
}
