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;
int main() {
  long n, k;
  cin >> n >> k;
  long j = 0;
  vector<long> v;
  for (int i = 1; i <= n; i++) {
    v.push_back(i);
  }
  swap(v[n - 1], v[n - k]);
  vector<int> temp;
  for (int i = 1; i < k; i++) {
    temp.push_back(v[n - k + i]);
  }
  sort(temp.begin(), temp.end());
  for (int i = 1; i < k; i += 2) {
    v[n - k + i] = temp[j];
    if (n - k + i + 1 < n) {
      v[n - k + i + 1] = temp[k - j - 2];
    }
    j++;
  }
  for (int i = 0; i < n; i++) {
    cout << v[i] << " ";
  }
}
