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 main() {
  int ytui, adsf, aargs, sadgs;
  int na, k;
  cin >> na >> k;
  int a[10000];
  if ((k + 1) % 2 != 1) {
    int s = (k + 1) / 2;
    int r = 1;
    cout << s;
    while (r != s) {
      cout << " " << s + r << " " << s - r;
      r++;
    }
    cout << " " << k + 1;
  } else {
    int s = (k + 1) / 2 + 1;
    int r = 1;
    cout << s;
    while (r != s) {
      cout << " " << s - r << " " << s + r;
      r++;
    }
  }
  for (int i = k + 2; i <= na; i++) cout << " " << i;
  return 0;
}
