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 n, m, x, y, q = 2, c, k;
long long a[100002];
int main() {
  cin >> n;
  cin >> m;
  c = min(n, m + 1);
  for (k = 1; k <= c / 2; k++) {
    cout << k << " " << c - k + 1 << " ";
  }
  if (c % 2 == 1) {
    cout << c / 2 + 1 << " ";
  }
  for (k = c; k <= n - 1; k++) {
    cout << k + 1 << " ";
  }
}
