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;
bool vis[100000];
int main() {
  int a, b, k = 1;
  cin >> a >> b;
  cout << 1 << " ";
  int c = b;
  for (int j = 0; j < c - 1; j++) {
    if (k - b >= 2 && !vis[k - b]) {
      vis[k - b] = true;
      cout << k - b << " ";
      k = k - b;
      --b;
    } else if (k + b <= a) {
      vis[k + b] = true;
      cout << k + b << " ";
      k = k + b;
      --b;
    }
  }
  for (int j = 2; j <= a; j++)
    if (!vis[j]) cout << j << " ";
  return 0;
}
