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 + 1;
int n, k;
vector<int> a;
int used[N], b[N];
int main() {
  cin >> n >> k;
  for (int i = n, q = 0; i >= 1 && q < n - k; i--, q++) a.push_back(i);
  a.push_back(1);
  for (int i = k - 1, r = 0; i; i--, r++)
    if (r % 2 == 0)
      a.push_back(a.back() + i);
    else
      a.push_back(a.back() - i);
  for (int i = 0; i < a.size(); i++) cout << a[i] << ' ';
  return 0;
}
