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() {
  cin.tie(NULL);
  ios_base::sync_with_stdio(0);
  int n, k, i = 1, j, z = 0;
  cin >> n >> k;
  j = n;
  while (k > 0) {
    if (z % 2 == 0) {
      cout << i++ << " ";
    } else {
      cout << j-- << " ";
    }
    ++z;
    --k;
  }
  if (z % 2 != 0) {
    while (i <= j) {
      cout << i++ << " ";
    }
  } else {
    while (j >= i) {
      cout << j-- << " ";
    }
  }
  return 0;
}
