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;
unsigned long long n, k, now = 1;
signed main() {
  ios::sync_with_stdio(0);
  cin >> n >> k;
  k--;
  for (unsigned long long i = 1; i <= k; i++) {
    if (i % 2)
      cout << now << " ";
    else {
      cout << n - now + 1 << " ";
      now++;
    }
  }
  if (k % 2 == 1) {
    for (unsigned long long i = n - k / 2; i >= k / 2 + 2; i--) {
      cout << i << " ";
    }
  } else {
    for (unsigned long long i = k / 2 + 1; i <= n - k / 2; i++) {
      cout << i << " ";
    }
  }
  return 0;
}
