CF195B.After Training

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.

欧洲足球锦标赛的一次训练结束后，瓦莱里克受命收集足球并将它们分类放入篮子中。整个体育场共有 $n$ 个球和 $m$ 个篮子。这些篮子从左到右排成一排，并依次编号为 $1$ 到 $m$。球也依次编号为 $1$ 到 $n$。

瓦莱里克决定按球编号递增的顺序对球进行分类，具体方案如下：他将每个新球放入当前球数最少的篮子中；若存在多个这样的篮子，则选择最靠近中间位置的那个篮子。也就是说，他选择使表达式 最小的篮子，其中 $i$ 表示篮子的编号；若此时仍有多个候选篮子，则选择编号最小的那个篮子。

请对每个球输出其根据瓦莱里克方案所放入的篮子编号。

注意：球是按编号递增的顺序依次放入篮子的，即先放编号为 $1$ 的球，再放编号为 $2$ 的球，依此类推。

The first line contains two space-separated integers n, m (1 ≤ n, m ≤ 105) — the number of balls and baskets, correspondingly.

第一行包含两个用空格分隔的整数 $n$、$m$（$1 ≤ n, m ≤ 10^5$），分别表示球的数量和篮子的数量。

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

输出 n 个数字，每行一个。第 i 行必须包含第 i 个球所在的篮子的编号。