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() {
  int n, k;
  cin >> n >> k;
  if (k == 1)
    for (int i = 0; i < n; i++) cout << i + 1 << " ";
  else {
    int g = (n + 1) / 2, x = 1, l = (n + 1) / 2, gr = (n + 1) / 2,
        p = (g + 1) / 2;
    for (int i = 0; i < n; i++) {
      if (i == 0) {
        cout << g << " ";
        k--;
      } else {
        if (k > 0 && i % 2) {
          cout << g + x << " ";
          gr = g + x;
          p = gr;
          k--;
        }
        if (k > 0 && !(i % 2)) {
          cout << g - x << " ";
          k--;
          l = g - x;
          p = l;
          x++;
        }
        if (k <= 0) {
          if (p == gr) {
            gr++;
            while (gr <= n) {
              cout << gr++ << " ";
            }
            l--;
            while (l > 0) {
              cout << l-- << " ";
            }
          } else {
            l--;
            while (l > 0) {
              cout << l-- << " ";
            }
            gr++;
            while (gr <= n) {
              cout << gr++ << " ";
            }
          }
          break;
        }
      }
    }
  }
}
