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 n, k, x;
int main() {
  x = 1;
  map<int, int> m;
  cin >> n >> k;
  cout << x << " ", m[x]++;
  int y = k, j = 0;
  while (k--) {
    if (j % 2)
      x -= y, cout << x << " ", m[x]++;
    else if (!(j % 2))
      x += y, cout << x << " ", m[x]++;
    y--;
    if (y <= 0) y = k;
    j++;
  }
  for (int i = 1; i <= n; i++)
    if (!m[i]) cout << i << " ";
  return 0;
}
