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 arr[100005];
void B() {
  int n, k;
  cin >> n >> k;
  if (k == 1) {
    for (int i = 1; i <= n; i++) cout << i << " ";
  } else {
    int i1 = 1;
    int i2 = n;
    int con = n;
    for (int i = 0; i < n - k; i++) {
      cout << i2 << " ";
      i2--;
      con--;
    }
    int odd = 0;
    while (con--) {
      if (odd == 0) {
        cout << i1 << " ";
        i1++;
        odd = 1;
      } else {
        cout << i2 << " ";
        i2--;
        odd = 0;
      }
    }
  }
}
int main() {
  B();
  return 0;
}
