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, k, tmp, tmp2;
  bool mark[100005];
  int save[100005];
  memset(mark, 0, sizeof(mark));
  cin >> n >> k;
  tmp = 1;
  printf("%d ", tmp);
  mark[tmp] = 1;
  for (int i = 0; i <= k - 1; i++) {
    if (tmp - (k - i) <= 0 || mark[tmp - (k - i)]) {
      tmp += (k - i);
    } else
      tmp -= k - i;
    mark[tmp] = 1;
    printf("%d", tmp);
    if (k != n - 1)
      printf(" ");
    else {
      if (i != k - 1)
        printf(" ");
      else
        printf("\n");
    }
  }
  int nn = 0;
  for (int i = 1; i <= n; i++) {
    if (!mark[i]) {
      save[nn++] = i;
    }
  }
  for (int i = 0; i < nn; i++) {
    printf("%d", save[i]);
    if (i != nn - 1)
      printf(" ");
    else
      printf("\n");
  }
  return 0;
}
