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() {
  long int n, k;
  cin >> n >> k;
  long int arr[k + 1];
  bool visited[n + 1];
  for (long int i = 1; i <= n; ++i) visited[i] = 0;
  long int value = k + 1;
  long int diff = k;
  long int check = 1;
  for (long int i = k + 1; i >= 1; i--) {
    arr[i] = value;
    visited[value] = 1;
    if (check % 2)
      value = value - diff;
    else
      value = value + diff;
    check++;
    diff--;
  }
  for (long int i = 1; i <= k + 1; i++) cout << arr[i] << " ";
  for (long int i = k + 2; i <= n; i++) cout << i << " ";
  return 0;
}
