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;
void file(const string& name1, const string& name2) {
  freopen((name1 + ".in").c_str(), "r", stdin);
  freopen((name2 + ".out").c_str(), "w", stdout);
}
const int MAXN = 100005;
int a[MAXN];
int main() {
  int n, k;
  cin >> n >> k;
  int cnt = 1;
  for (int i = 0; i < k; ++i) {
    if (i % 2 == 0)
      a[i] = cnt;
    else
      a[i] = n - cnt + 1;
    if (i % 2 == 1) cnt++;
  }
  if (k % 2 == 0) {
    cnt = n - cnt + 1;
    for (int i = k; i < n; ++i) {
      a[i] = cnt;
      cnt--;
    }
  } else {
    cnt++;
    for (int i = k; i < n; ++i) {
      a[i] = cnt;
      cnt++;
    }
  }
  for (int i = 0; i < n; ++i) cout << a[i] << ' ';
  return 0;
}
