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>
#pragma comment(linker, "/STACK:256000000")
using namespace std;
int n, k;
int ans[100010];
void build_ans(int m) {
  int cur = 0;
  int dt = 2;
  for (int i = 1; i <= m; i++) {
    ans[cur] = i;
    cur += dt;
    if (cur >= m) {
      cur = m - 1 - (m % 2);
      dt = -2;
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cin >> n >> k;
  build_ans(k + 1);
  for (int i = 1; i < n - k; i++) cout << i << " ";
  for (int i = 0; i < k + 1; i++) cout << ans[i] + n - k - 1 << " ";
  return 0;
}
