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;
const int MX = 1e5 + 9;
const long long mod = 1e9 + 7;
long long n, k, vis[MX], a, b;
int main() {
  scanf("%lld%lld", &n, &k);
  a = 1;
  b = n;
  for (int j = 0; j < k; j++) {
    if (j % 2)
      vis[a] = 1, cout << a++ << " ";
    else
      vis[b] = 1, cout << b-- << " ";
  }
  if (k % 2 == 0)
    for (int i = 1; i <= n; i++)
      if (!vis[i]) cout << i << " ";
  if (k % 2 == 1)
    for (int i = n; i >= 1; i--)
      if (!vis[i]) cout << i << " ";
}
