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 node {
  int a, b;
  bool flag;
};
int main() {
  long long a, b, i, j, k, m, t, n, p, q, x, y;
  string s;
  p = 0;
  while (cin >> p >> q) {
    a = 1;
    b = 1 + q;
    while (a < b) cout << a++ << " " << b-- << " ";
    if (a == b) cout << a << " ";
    for (i = 2 + q; i <= p; i++) cout << i << " ";
    cout << endl;
  }
  return 0;
}
