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;
const int INF = -1u / 2;
const int size = 0;
const int MOD = 1;
int main(int argc, char const *argv[]) {
  int n, m;
  scanf("%d%d", &n, &m);
  int s = 1;
  int e = n;
  int k = m;
  while (1) {
    if (k > 0) {
      printf("%d ", e--);
      k--;
      if (k == 0) {
        for (int i(0); i <= (n - (m - k)) - 1; ++i) printf("%d ", e--);
        break;
      }
    }
    if (k > 0) {
      printf("%d ", s++);
      k--;
      if (k == 0) {
        for (int i(0); i <= (n - (m - k)) - 1; ++i) printf("%d ", s++);
        break;
      }
    }
  }
  return 0;
}
