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;
  cin >> n >> k;
  vector<int> a(n);
  int curr_e = n;
  int curr_o = 1;
  bool z = false;
  for (int i = 0; i < k; ++i) {
    if (i % 2 == 1) {
      a[i] = curr_o;
      ++curr_o;
      z = false;
    } else {
      a[i] = curr_e;
      --curr_e;
      z = true;
    }
  }
  for (int i = k; i < n; ++i) {
    if (z) {
      a[i] = a[i - 1] - 1;
    } else
      a[i] = a[i - 1] + 1;
  }
  for (auto i : a) cout << i << " ";
  return 0;
}
