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, k;
vector<int> vec;
int main() {
  cin >> n >> k;
  int n1 = 1;
  int n2 = n;
  int x = k / 2;
  while (x--) {
    vec.push_back(n1);
    vec.push_back(n2);
    n1++;
    n2--;
  }
  for (int i = n2; i >= n1 && (k % 2 == 0); i--) {
    vec.push_back(i);
  }
  for (int i = n1; i <= n2 && k % 2; i++) {
    vec.push_back(i);
  }
  for (int i = 0; i < vec.size(); i++) {
    cout << vec[i] << " ";
  }
  cout << endl;
  return 0;
}
