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;
template <class T>
inline T gcd(T a, T b) {
  return b ? gcd(b, a % b) : a;
}
long long MOD = 1000000007;
int main() {
  int n, k, counter = 1, dis, diff, i, j, curr, flag;
  flag = 1;
  scanf("%d", &n);
  scanf("%d", &k);
  printf("%d ", 1);
  for (i = 1, j = 0, diff = n - 1; j < k - 1; j++, diff--) {
    printf("%d ", i + diff * flag);
    i = i + diff * flag;
    flag *= -1;
    counter++;
  }
  if (flag == 1 && counter != n) {
    i++;
    while (counter != n) {
      printf("%d ", i++);
      counter++;
    }
  } else if (flag == -1 && counter != n) {
    i--;
    while (counter != n) {
      printf("%d ", i--);
      counter++;
    }
  }
  return 0;
}
