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 n, i, j, k, ct, b, lv;
vector<int> inc, decr;
int main() {
  cin >> n >> k;
  for (i = 1; i <= n; i++) inc.push_back(i);
  for (i = n; i > 0; i--) decr.push_back(i);
  ct = 0;
  i = 0;
  j = 0;
  lv = 0;
  k--;
  while (ct < k) {
    if (lv == 0) {
      cout << inc[i] << ' ';
      i++;
      lv = 1;
    } else {
      cout << decr[j] << ' ';
      j++;
      lv = 0;
    }
    ct++;
  }
  b = ct;
  while (b < n) {
    if (lv == 0) {
      cout << inc[i] << ' ';
      i++;
    } else {
      cout << decr[j] << ' ';
      j++;
    }
    b++;
  }
}
