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;
;
struct _dbg {
  template <class T>
  _dbg& operator,(const T& v) {
    cerr << v << " ";
    return *this;
  };
};
_dbg _d;
int main() {
  int N, K, i = 0;
  cin >> N >> K;
  for (; i < N - K; ++i) cout << i + 1 << ' ';
  for (int j = 0, _j = (K); j < _j; ++j) cout << (j & 1 ? ++i : N--) << ' ';
};
