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() {
  int N, K;
  cin >> N >> K;
  for (int i = 1; i <= N - K; ++i) {
    cout << i << ' ';
  }
  int prev = N - K;
  int diff = K;
  for (int i = 0; i < K; ++i) {
    cout << prev + diff << ' ';
    prev = prev + diff;
    if (diff < 0)
      ++diff;
    else
      --diff;
    diff *= -1;
  }
  return 0;
}
