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 N = 1e5 + 5;
int arr[N];
int n, k;
int main() {
  ios_base::sync_with_stdio(0);
  ;
  cin >> n >> k;
  int l = 1, r = n;
  int mark;
  for (int i = 1; i <= n; i++) {
    if (k) {
      if (i & 1)
        arr[i] = l++;
      else
        arr[i] = r--;
      --k;
    }
    if (k == 0) {
      mark = i;
      break;
    }
  }
  if (mark % 2) {
    for (int i = mark + 1; i <= n; i++) arr[i] = l++;
  } else {
    for (int i = mark + 1; i <= n; i++) arr[i] = r--;
  }
  for (int i = 1; i <= n; i++) cout << arr[i] << " ";
}
