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;
bool mark[100002];
std::vector<int> ans;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n, k;
  cin >> n >> k;
  int cur = 1, l = 2, r = n;
  if (k == 1) {
    for (int i = 1; i < n + 1; ++i) cout << i << " ";
    return 0;
  }
  if (k == 2) {
    cout << n << " 1 ";
    for (int i = 2; i < n; ++i) cout << i << " ";
    return 0;
  }
  ans.push_back(1);
  mark[1] = 1;
  while (k > 2) {
    if (cur & 1)
      ans.push_back(r), mark[r--] = 1;
    else
      ans.push_back(l), mark[l++] = 1;
    cur++;
    k--;
  }
  for (auto &x : ans) cout << x << " ";
  if (cur & 1) {
    for (int i = n; i >= 1; --i)
      if (!mark[i]) cout << i << " ";
  } else {
    for (int i = 1; i < n + 1; ++i)
      if (!mark[i]) cout << i << " ";
  }
  return 0;
}
