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 GCD(int a, int b) {
  if (!a) return b;
  return GCD(b % a, a);
}
int main() {
  clock_t startTime = clock();
  ios_base::sync_with_stdio(false);
  int n, k;
  cin >> n >> k;
  vector<int> ans(n);
  int l = 1, r = n;
  for (int i = (0); i < (int)(k); i++) {
    if (i % 2 == 0) {
      ans[i] = l;
      l++;
    } else {
      ans[i] = r;
      r--;
    }
  }
  for (int i = (k); i < (int)(n); i++) {
    if (k % 2 == 0)
      ans[i] = r--;
    else
      ans[i] = l++;
  }
  for (int i = (0); i < (int)(n); i++) cout << ans[i] << " ";
  clock_t endTime = clock();
  cerr << "\nTime:" << double(endTime - startTime) / CLOCKS_PER_SEC
       << " seconds\n";
  return 0;
}
