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;
const long long int MOD = 1e9 + 7;
void solve() {
  int n, k;
  cin >> n >> k;
  vector<int> v(n);
  for (int i = 1; i <= n; i++) v[i - 1] = i;
  int i = 0, j = n - 1;
  while (true) {
    if (k == 1) {
      while (i <= j) {
        cout << v[i++] << ' ';
      }
      break;
    } else if (k == 0) {
      while (i <= j) {
        cout << v[j--] << ' ';
      }
      break;
    } else {
      cout << v[i++] << ' ' << v[j--] << ' ';
      k -= 2;
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  solve();
}
