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>
int find(double a[], int l, double b) {
  int c = 0;
  for (int i = 1; i <= l; i++)
    if (a[i - 1] == b) c++;
  return c;
}
using namespace std;
int main() {
  int a, b, c = 1, q = 1;
  cin >> a >> b;
  cout << q << ' ';
  for (int i = b; i >= 1; i--) {
    if (c) {
      q += i;
      cout << q << ' ';
    } else {
      q -= i;
      cout << q << ' ';
    }
    c = !c;
  }
  for (int y = b + 2; y <= a; y++) cout << y << ' ';
  return 0;
}
