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 a[100050], b[100050] = {0};
int main() {
  int i, n, k, l = 1, m = 2, p = 1;
  scanf("%d%d", &n, &k);
  for (i = 0; i < n; i++) {
    a[i] = i + 1;
  }
  m = k;
  for (int j = k; k > 1; k = k - 2) {
    b[l] = a[j];
    l++;
    b[l] = a[p];
    j--;
    p++;
    l++;
  }
  if (k == 1) b[l] = a[p];
  printf("1");
  for (i = 1; i < n; i++) {
    if (b[i] == 0) {
      printf(" %d", m + 2);
      m++;
    } else
      printf(" %d", b[i]);
  }
  printf("\n");
}
