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;
using ll = long long;
using ull = unsigned long long;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  int n, k;
  cin >> n >> k;
  int ara[n + 1];
  for (int i = 0; i < n; ++i) ara[i] = i + 1;
  int sz = k, first = 0, last = n - 1, cnt = 0;
  bool accf = 1, accl = 0;
  while (sz--) {
    if (accf) {
      cout << ara[first] << " ";
      ++cnt;
      ++first;
      accf = 0;
      accl = 1;
    } else if (accl) {
      cout << ara[last] << " ";
      ++cnt;
      --last;
      accf = 1;
      accl = 0;
    }
  }
  if (!(cnt % 2)) {
    for (int i = last; i >= first; --i) cout << ara[i] << " ";
  } else {
    for (int i = first; i <= last; ++i) cout << ara[i] << " ";
  }
  cout << "\n";
}
