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, m;
  while (cin >> n >> m) {
    int i = 1;
    for (i; i <= m; i++) {
      if (i != 1) printf(" ");
      if (i % 2 == 1)
        printf("%d", i / 2 + 1);
      else
        printf("%d", n - i / 2 + 1);
    }
    if (i % 2 == 1) {
      int end = (i + 1) / 2;
      for (int j = n - (i + 1) / 2 + 1; j >= end; j--) {
        printf(" %d", j);
      }
      printf("\n");
    } else {
      int end = n - (i + 1) / 2 + 1;
      for (int j = (i - 1) / 2 + 2; j <= end; j++) {
        printf(" %d", j);
      }
      printf("\n");
    }
  }
}
