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 int MAX = 1e5 + 10;
bool used[MAX];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  int n, k;
  cin >> n >> k;
  int arr[n];
  int low = 1;
  int MAX = n;
  for (int i = 0; i < (int)(k); ++i) {
    if (i % 2 == 0) {
      used[low] = 1;
      cout << low++ << ' ';
    } else {
      used[MAX] = 1;
      cout << MAX-- << ' ';
    }
  }
  if (k % 2 != 0) {
    for (int i = 0; i < n; ++i) {
      if (!used[i + 1]) {
        cout << i + 1 << ' ';
      }
    }
  } else {
    for (int i = n - 1; i >= 0; --i) {
      if (!used[i + 1]) {
        cout << i + 1 << ' ';
      }
    }
  }
}
