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 n, k;
bool used[(int)1e5 + 10];
vector<int> arr;
int main() {
  cin >> n >> k;
  used[n] = true;
  arr.push_back(n);
  bool low = true;
  for (int dist = k; dist >= 2; --dist) {
    if (low) {
      used[arr.back() - dist] = true;
      arr.push_back(arr.back() - dist);
    } else {
      used[arr.back() + dist] = true;
      arr.push_back(arr.back() + dist);
    }
    low ^= 1;
  }
  for (int i = n; i >= 1; --i)
    if (!used[i]) arr.push_back(i);
  for (int i = 0; i < arr.size(); ++i) {
    cout << arr[i];
    if (i + 1 < arr.size())
      cout << ' ';
    else
      cout << '\n';
  }
}
