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;
long long max(long long x, long long y) { return x > y ? x : y; }
long long min(long long x, long long y) { return x < y ? x : y; }
int main() {
  ios::sync_with_stdio(false);
  int n, k;
  cin >> n >> k;
  int s = 1, e = n;
  for (int i = 1; i <= (n - 1 - k); i++) {
    cout << i << ' ';
    s++;
  }
  while (e - s >= 1) {
    cout << s << ' ' << e << ' ';
    s++;
    e--;
  }
  if (s == e) cout << s;
}
