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() {
  long n, k, mid, incr, i, sign;
  scanf("%ld %ld", &n, &k);
  if ((k + 1) % 2 == 0) {
    mid = (k + 1) / 2;
    sign = 1;
  } else {
    mid = (k + 1) / 2 + 1;
    sign = -1;
  }
  printf("%ld ", mid);
  incr = 1;
  long num;
  for (i = 1; i <= k; i++) {
    num = mid + sign * incr;
    printf("%ld ", num);
    sign *= -1;
    incr++;
    mid = num;
  }
  num++;
  for (i = k + 1; i < n; i++) {
    printf("%ld ", num);
    num++;
  }
  return 0;
}
