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(0);
  cin.tie(0);
  int n, k;
  while (cin >> n >> k) {
    cout << n;
    int x = n - 1, y = 1;
    while (k > 2) {
      cout << " " << y << " " << x;
      x -= 1;
      y += 1;
      k -= 2;
    }
    if (k == 1) {
      for (int i = x; i >= y; i--) cout << " " << i;
    } else if (k == 2) {
      int a = y + 1, b = y;
      for (int i = x; i > a; i--) cout << " " << i;
      cout << " " << b << " " << a;
    }
    cout << endl;
  }
  return 0;
}
