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 p[100005];
int main() {
  int n, k;
  while (cin >> n >> k) {
    if (k == 1) {
      for (int i = 1; i <= n; i++) cout << i << " ";
      cout << endl;
    } else {
      bool flag = true;
      int a = n - 1;
      p[1] = 1;
      for (int i = 2; i <= n; i++) {
        if (flag) {
          p[i] = p[i - 1] + a;
          a--;
          flag = false;
        } else {
          p[i] = p[i - 1] - a;
          a--;
          flag = true;
        }
      }
      for (int i = 1; i <= k; i++) {
        cout << p[i] << " ";
      }
      int x = p[k];
      if (k % 2) {
        for (int i = k + 1; i <= n; i++) cout << ++x << " ";
      } else {
        for (int i = k + 1; i <= n; i++) cout << --x << " ";
      }
      cout << endl;
    }
  }
}
