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;
  if (k < 4) {
    for (int i = 1; i <= n; i++) {
      if (i == n) {
        if (i - 1 == k) {
          cout << i << " ";
          if (i == 2)
            continue;
          else
            cout << 2 << " ";
        } else {
          if (i == 2) continue;
          cout << i << endl;
        }
      } else {
        if (i - 1 == k) {
          cout << i << " ";
          if (i == 2)
            continue;
          else
            cout << 2 << " ";
        } else {
          if (i == 2) continue;
          cout << i << " ";
        }
      }
    }
  } else {
    int tmp = n;
    for (int i = 1; i <= (n - ((k - 1) / 2 + 2)); i++) {
      if (i <= (k - 1) / 2) {
        cout << i << " " << tmp << " ";
        tmp--;
      } else
        cout << i << " ";
    }
    if (k % 2) {
      cout << n - (k - 1) / 2 - 1 << " " << n - (k - 1) / 2 << endl;
    } else {
      cout << n - (k - 1) / 2 << " " << n - (k - 1) / 2 - 1 << endl;
    }
  }
  return 0;
}
