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;
const int maxn = 100 * 1000 + 100;
int n, k;
int ans[maxn];
vector<int> a;
int main() {
  ios ::sync_with_stdio(false);
  cin >> n >> k;
  for (int i = n; i > k + 1; i--) ans[n - i] = i;
  int ind1 = k + 1, ind2 = 1, t = 0;
  while (ind2 <= ind1) {
    if (t % 2 == 0) {
      a.push_back(ind1);
      ind1--;
    } else {
      a.push_back(ind2);
      ind2++;
    }
    t++;
  }
  for (int i = 0; i < a.size(); i++) ans[n - k - 1 + i] = a[i];
  for (int i = 0; i < n; i++) cout << ans[i] << " ";
  return 0;
}
