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() {
  int n, k;
  while (cin >> n >> k) {
    int a = 1, b = n, cnt = 0;
    vector<int> v;
    while (cnt < k / 2) {
      v.push_back(a);
      v.push_back(b);
      a++;
      b--;
      cnt++;
    }
    if (k % 2) {
      while (v.size() < n) {
        v.push_back(a);
        a++;
      }
    } else {
      while (v.size() < n) {
        v.push_back(b);
        b--;
      }
    }
    for (int i = 0; i < v.size(); i++) {
      if (i) {
        cout << " ";
      }
      cout << v[i];
    }
    cout << endl;
  }
  return 0;
}
