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;
  while (cin >> n >> k) {
    vector<bool> used(n + 1, false);
    int l = 1, r = n;
    for (int i = 0; i < k; i++) {
      if (i % 2 == 0) {
        cout << l << " ";
        used[l] = true;
        l += 1;
      } else {
        cout << r << " ";
        used[r] = true;
        r -= 1;
      }
    }
    if (k % 2 == 0) {
      for (int i = n; i > 0; i--) {
        if (!used[i]) {
          cout << i << " ";
        }
      }
    } else {
      for (int i = 1; i < used.size(); i++) {
        if (!used[i]) {
          cout << i << " ";
        }
      }
    }
    cout << endl;
  }
  return 0;
}
