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() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  ;
  long long n, k;
  cin >> n >> k;
  long long w = 0, s = 1, s1 = 0, w1 = 0;
  for (long long i = 0; i <= (k - 1); i++) {
    if (i % 2 == 0) {
      cout << (s) << " ";
      s++;
    } else {
      cout << (n - s1) << " ";
      s1++;
    }
    w = s;
    w1 = s1;
  }
  if (k % 2 == 1) {
    for (long long i = w; i <= (n - w1); i++) {
      cout << i << " ";
    }
  } else {
    for (long long i = n - w1; i >= w; i--) {
      cout << i << " ";
    }
  }
}
