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 N = 1e5 + 5;
const int alpha = 26;
const int dx[] = {2, 1, 2, -1, -2, 1, -2, -1};
const int dy[] = {1, 2, -1, 2, 1, -2, -1, -2};
bool used[N];
int main() {
  int n, k;
  cin >> n >> k;
  if (k == 1) {
    for (int i = 1; i <= n; i++) cout << i << " ";
    return 0;
  }
  int cnt = k;
  int cur = 1, l = 1;
  while (cnt > 0) {
    cout << cur << " ";
    used[cur] = 1;
    if (l % 2 == 1)
      cur += cnt;
    else
      cur -= cnt;
    l++;
    cnt--;
  }
  for (int i = 1; i <= n; i++)
    if (!used[i]) cout << i << " ";
}
