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 n, k;
vector<int> res;
void solve() {
  int flag = 1;
  int last = 1;
  res.push_back(1);
  for (int i = k; i > 0; i--) {
    last = last + flag * i;
    res.push_back(last);
    flag = -flag;
  }
  for (int i = k + 2; i <= n; i++) res.push_back(i);
}
int main() {
  cin >> n >> k;
  solve();
  vector<int>::iterator it;
  for (it = res.begin(); it != res.end() - 1; it++) {
    cout << (*it) << " ";
  }
  cout << (*it) << endl;
  return 0;
}
