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(void) {
  int n;
  int k;
  cin >> n >> k;
  int num1 = 2, k1 = k;
  k--;
  int num2 = n;
  int count = 1;
  cout << 1 << " ";
  while (k--) {
    if (count & 1)
      cout << num2 << " ", num2--;
    else
      cout << num1 << " ", num1++;
    count++;
  }
  for (int i = k1 + 1; i <= n; i++) {
    if (k1 & 1)
      cout << num1 << " ", num1++;
    else
      cout << num2 << " ", num2--;
  }
  puts("");
  return 0;
}
