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;
  int a[n + 1];
  for (int i = 1; i <= n; i++) a[i] = i;
  vector<int> v;
  for (int i = 1; i <= n - 1 - k; i++) v.push_back(a[i]);
  for (int i = n - k, j = n; i < j; i++, j--) {
    v.push_back(a[i]);
    v.push_back(a[j]);
  }
  if (v.size() != n) v.push_back(v[v.size() - 1] - 1);
  for (int i = 0; i < v.size(); i++) cout << v[i] << " ";
}
