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 mini(int a, int b) { return a < b ? a : b; }
long long lmini(long long a, long long b) { return a < b ? a : b; }
int maxi(int a, int b) { return a > b ? a : b; }
long long lmaxi(long long a, long long b) { return a > b ? a : b; }
int main() {
  int n, k, i, m, prev;
  scanf("%d%d", &n, &k);
  cout << 1 << " ";
  bool flag = 0;
  m = k;
  prev = 1;
  for (i = 2; i <= n; i++) {
    if (k != 0) {
      if (flag == 0) {
        cout << prev + k << " ";
        flag = 1;
        prev = prev + k;
        k--;
        ;
      } else {
        cout << prev - k << " ";
        flag = 0;
        prev = prev - k;
        k--;
      }
    } else {
      cout << 2 + m << " ";
      m++;
    }
  }
  return 0;
}
