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, up;
  vector<int> v;
  cin >> n >> k;
  int tot = 0;
  for (int i = 1, j = 1; tot < k; i++) {
    if (i % 2)
      v.push_back(j);
    else {
      v.push_back(n - j + 1);
      j++;
    }
    tot++;
  }
  if (tot % 2)
    up = 1;
  else
    up = 0;
  if (up == 0)
    while (tot < n) {
      v.push_back(v[(int)v.size() - 1] - 1);
      tot++;
    }
  else
    while (tot < n) {
      v.push_back(v[(int)v.size() - 1] + 1);
      tot++;
    }
  for (int i = 0; i < (int)v.size(); i++) cout << v[i] << " ";
  return 0;
}
