After Training

题意翻译

有 $n$ 个球，要放入 $m$ 个篮筐中。对于每次的投放： $1$.放入已有球数最小的框中。 $2$.如有多种情况，选择最靠近中间的。 $3$.在同样靠近中间的球中，选择最靠左的。 问每个球应放入第几个框中。

题目描述

After a team finished their training session on Euro football championship, Valeric was commissioned to gather the balls and sort them into baskets. Overall the stadium has $ n $ balls and $ m $ baskets. The baskets are positioned in a row from left to right and they are numbered with numbers from $ 1 $ to $ m $ , correspondingly. The balls are numbered with numbers from $ 1 $ to $ n $ . Valeric decided to sort the balls in the order of increasing of their numbers by the following scheme. He will put each new ball in the basket with the least number of balls. And if he's got several variants, he chooses the basket which stands closer to the middle. That means that he chooses the basket for which  is minimum, where $ i $ is the number of the basket. If in this case Valeric still has multiple variants, he chooses the basket with the minimum number. For every ball print the number of the basket where it will go according to Valeric's scheme. Note that the balls are sorted into baskets in the order of increasing numbers, that is, the first ball goes first, then goes the second ball and so on.

输入输出格式

输入格式

The first line contains two space-separated integers $ n $ , $ m $ $ (1<=n,m<=10^{5}) $ — the number of balls and baskets, correspondingly.

输出格式

Print $ n $ numbers, one per line. The $ i $ -th line must contain the number of the basket for the $ i $ -th ball.

输入输出样例

输入样例 #1

4 3

输出样例 #1

2
1
3
2

输入样例 #2

3 1

输出样例 #2

1
1
1