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 a, b, num = 1;
  bool biao[100100] = {0}, kk = 1;
  scanf("%d%d", &a, &b);
  printf("1 ");
  while (b != 1) {
    if (kk) {
      printf("%d ", num + b);
      num = num + b;
      biao[num] = 1;
      b--;
      kk = 0;
    } else {
      printf("%d ", num - b);
      num = num - b;
      biao[num] = 1;
      b--;
      kk = 1;
    }
  }
  for (int i = 2; i <= a; i++)
    if (biao[i] == 0) printf("%d ", i);
}
