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>
#pragma comment(linker, "/STACK:100000000")
using namespace std;
const bool db = false;
int n, k;
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 0; i < n - k; ++i) cout << i + 1 << " ";
  int last = n, cur = n - k + 1;
  for (int i = n - k; i < n; ++i)
    if (i % 2 != (n - k) % 2)
      cout << cur++ << " ";
    else
      cout << last-- << " ";
  getchar();
  getchar();
  return 0;
}
