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;
  cin >> n >> k;
  int a[n];
  a[0] = 1;
  int i = 1;
  bool f[n + 1];
  memset(f, 0, sizeof(f));
  while (k > 0) {
    if (i % 2 == 0) {
      a[i] = a[i - 1] - k;
      f[a[i]] = true;
      k--;
    } else {
      a[i] = a[i - 1] + k;
      f[a[i]] = true;
      k--;
    }
    i++;
  }
  f[1] = true;
  vector<int> l;
  for (int j = 1; j <= n; j++) {
    if (!f[j]) {
      l.push_back(j);
    }
  }
  int m = 0;
  for (int j = i; j < n; j++) {
    a[j] = l[m];
    m++;
  }
  for (int j = 0; j < n; j++) {
    cout << a[j] << " ";
  }
  return 0;
}
