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;
long long POS(long long x) {
  if (x > 0)
    return x;
  else
    return 0;
}
bool vis[100005];
int main() {
  int n, k, i = 1, c = 0, f = 1;
  cin >> n >> k;
  while (k >= 1) {
    cout << i << " ";
    vis[i] = true;
    if (f == 1) {
      i += k;
      f = 0;
    } else {
      i -= k;
      f = 1;
    }
    k--;
    c++;
  }
  for (int j = 1; j <= n && c < n; j++) {
    if (!vis[j]) {
      cout << j << " ";
    }
  }
  return 0;
}
