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 i, j, k, n, second;
  cin >> n >> k;
  if (k == 1) {
    for (i = 1; i <= n; i++) cout << i << " ";
    return 0;
  }
  int inc, start;
  if ((k + 1) % 2 == 0) {
    start = (k + 1) / 2;
    inc = 1;
  } else {
    start = ((k + 1) / 2) + 1;
    inc = 0;
  }
  int count = 1;
  while (count <= k) {
    cout << start << " ";
    if (inc == 1) {
      start = start + count;
      inc = 0;
    } else {
      start = start - count;
      inc = 1;
    }
    count++;
  }
  cout << start << " ";
  for (i = k + 2; i <= n; i++) cout << i << " ";
}
