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 double PI = 2.0 * acos(0.0);
const int INF = 1000 * 1000 * 1000;
const int maxn = 100009;
bool vis[maxn];
vector<int> ans;
int main() {
  int N, K;
  cin >> N >> K;
  memset(vis, false, sizeof vis);
  ans.push_back(1);
  vis[1] = true;
  int p = 2;
  int KK = K + 1;
  for (int i = 0; i < K; i++) {
    if (i % 2 == 0) {
      vis[KK] = true;
      ans.push_back(KK);
      KK--;
    } else {
      vis[p] = true;
      ans.push_back(p);
      p++;
    }
  }
  for (int i = 1; i <= N; i++)
    if (vis[i] == false) ans.push_back(i);
  cout << ans[0];
  for (int i = 1; i < N; i++) cout << " " << ans[i];
  cout << endl;
  return 0;
}
