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;
using ll = long long;
int main() {
  int n, k;
  cin >> n >> k;
  int i = 1, j = n;
  int cnt = 0;
  vector<int> v;
  for (int p = 1; p <= n; p++) {
    if (p % 2 != 0) {
      cout << i << " ";
      i++;
      cnt++;
      if (cnt == k) {
        for (int q = i; q <= j; q++) cout << q << " ";
        break;
      }
    } else if (p % 2 == 0) {
      cout << j << " ";
      j--;
      cnt++;
      if (cnt == k) {
        for (int q = j; q >= i; q--) cout << q << " ";
        break;
      }
    }
  }
  return 0;
}
