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;
void task() {
  ios_base::sync_with_stdio(0);
  cin >> n >> k;
  int left = 0;
  int right = n + 1;
  int last = 1;
  for (int i = 0; i < k; ++i)
    cout << (last = (i % 2 ? --right : ++left)) << ' ';
  int d = k % 2 ? 1 : -1;
  for (int i = last + d; i < right && left < i; i += d) cout << i << ' ';
}
int main() {
  task();
  return 0;
}
