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() {
  long long n, k;
  while (cin >> n >> k) {
    int st = 1;
    cout << st;
    int cnt = 0;
    set<int> s;
    s.insert(st);
    while (k--) {
      if (cnt % 2 == 0) {
        cout << " " << st + k + 1;
        st = st + k + 1;
        s.insert(st);
      } else {
        cout << " " << st - k - 1;
        st = st - k - 1;
        s.insert(st);
      }
      cnt++;
    }
    for (int i = 1; i <= n; i++) {
      if (s.find(i) == s.end()) {
        cout << " " << i;
      }
    }
    cout << endl;
  }
  return 0;
}
