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 maxn = 100005;
int n, m;
int main() {
  while (scanf("%d%d", &n, &m) != EOF) {
    printf("1 ");
    int flag = 0;
    for (int i = m, idx = 1; i >= 1; i--) {
      if (flag == 0)
        idx += i;
      else
        idx -= i;
      flag = 1 - flag;
      printf("%d ", idx);
    }
    for (int i = m + 2; i <= n; i++) {
      printf("%d ", i);
    }
  }
  return 0;
}
