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>
int main() {
  int n, k;
  while (~scanf("%d%d", &n, &k)) {
    printf("%d", 1);
    int L = 2, R = k + 1;
    int hehe = R;
    while (L < R) {
      printf(" %d %d", R, L);
      R--;
      L++;
    }
    if (L == R) {
      printf(" %d", L);
    }
    for (int i = hehe + 1; i <= n; i++) {
      printf(" %d", i);
    }
    printf("\n");
  }
  return 0;
}
