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 ans[100005], n, k;
bool v[100005];
int main() {
  cin >> n >> k;
  int cha = k;
  ans[1] = 1;
  v[1] = 1;
  for (int i = 2; i <= k + 1; i++) {
    if (i % 2 == 0)
      ans[i] = ans[i - 1] + cha;
    else
      ans[i] = ans[i - 1] - cha;
    cha--;
  }
  int s = k + 1;
  for (int i = 1; i <= n; i++) {
    if (ans[i] <= 0) {
      ans[i] = ++s;
    }
    printf("%d ", ans[i]);
  }
}
