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;
bool vis[100010];
int main() {
  int n, k;
  cin >> n >> k;
  vis[1] = 1, vis[k + 1] = 1;
  cout << 1 << " " << k + 1 << " ";
  int pos = 1 + k, pm = -1;
  for (int j = k - 1; j >= 1; j--) {
    pos = pos + pm * j;
    if (pos <= 0 || pos > n) {
      pm *= -1;
      pos = pos + pm * j;
    }
    vis[pos] = 1;
    cout << pos << " ";
    pm *= -1;
  }
  for (int i = pos - 1; i >= 2; i--) {
    if (!vis[i]) cout << i << " ";
    vis[i] = 1;
  }
  for (int i = 2; i <= n; i++) {
    if (!vis[i]) cout << i << " ";
  }
  return 0;
}
