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(NULL);
  ;
  int n, k;
  cin >> n >> k;
  vector<int> v;
  bool flag = 1;
  int i = 1, j = n;
  while (k--) {
    if (flag) {
      v.push_back(i);
      i++;
      flag = 0;
    } else {
      v.push_back(j);
      j--;
      flag = 1;
    }
  }
  if (flag == 0) {
    j++;
    while (i != j) {
      v.push_back(i);
      i++;
    }
  } else {
    i--;
    while (i != j) {
      v.push_back(j);
      j--;
    }
  }
  for (int i = 0; i < v.size(); i++) {
    cout << v[i] << " ";
  }
}
