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;
deque<int> q;
int main() {
  int n, k;
  scanf("%d %d", &n, &k);
  for (int i = 0; i < n; i++) q.push_back(i + 1);
  bool top = true;
  if (k % 2 != 0) {
    while (k--) {
      if (top) {
        cout << q.front() << " ";
        q.pop_front();
        top = false;
      } else {
        cout << q.back() << " ";
        q.pop_back();
        top = true;
      }
    }
    while (!q.empty()) {
      cout << q.front() << " ";
      q.pop_front();
    }
  } else {
    while (k--) {
      if (top) {
        cout << q.front() << " ";
        q.pop_front();
        top = false;
      } else {
        cout << q.back() << " ";
        q.pop_back();
        top = true;
      }
    }
    while (!q.empty()) {
      cout << q.back() << " ";
      q.pop_back();
    }
  }
  return 0;
}
