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() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  int n, k;
  cin >> n >> k;
  int* arr = new int[n];
  for (int i = 0; i < n - k; i++) arr[i] = i + 1;
  int p = 0;
  for (int i = n - k; i < n; i++, p++) {
    if (p % 2 == 0) {
      arr[i] = arr[i - 1] + k - p;
    } else {
      arr[i] = arr[i - 1] - k + p;
    }
  }
  for (int i = 0; i < n; i++) cout << arr[i] << " ";
  delete[] arr;
  return 0;
}
