Two Teams

## Description 有 $n$ 个人站成一排，他们每个人都有一个能力值，能力值互不相同。 有两个教练，分别是 $1$ 队教练和 $2$ 队教练。由 $1$ 队教练先挑，每次教练会将场上剩下的人中能力值最高的和他左右各 $k$ 个人从场上挑出，加入自己的队伍，然后由另一名教练再挑。 在挑选时如果一侧不足 $k$ 个人则将这些人都挑入队伍。 请求出每个人最终加入的是哪个队伍 ## Input 第一行是两个整数 $n,~k$ 下面一行是一个 $1$ 到 $n$ 的排列，描述每个人的能力值 ## Output 输出一行一个字符串。如果第 $i$ 个人最终加入 $1$ 队，则字符串第 $i$ 位为 $1$，否则为 $2$。 ## Limitation $1~\leq~k~\leq~n~\leq~2~\times~10^5$ Translated By @ 一扶苏一

There are $ n $ students standing in a row. Two coaches are forming two teams — the first coach chooses the first team and the second coach chooses the second team. The $ i $ -th student has integer programming skill $ a_i $ . All programming skills are distinct and between $ 1 $ and $ n $ , inclusive. Firstly, the first coach will choose the student with maximum programming skill among all students not taken into any team, and $ k $ closest students to the left of him and $ k $ closest students to the right of him (if there are less than $ k $ students to the left or to the right, all of them will be chosen). All students that are chosen leave the row and join the first team. Secondly, the second coach will make the same move (but all students chosen by him join the second team). Then again the first coach will make such move, and so on. This repeats until the row becomes empty (i. e. the process ends when each student becomes to some team). Your problem is to determine which students will be taken into the first team and which students will be taken into the second team.

The first line of the input contains two integers $ n $ and $ k $ ( $ 1 \le k \le n \le 2 \cdot 10^5 $ ) — the number of students and the value determining the range of chosen students during each move, respectively. The second line of the input contains $ n $ integers $ a_1, a_2, \dots, a_n $ ( $ 1 \le a_i \le n $ ), where $ a_i $ is the programming skill of the $ i $ -th student. It is guaranteed that all programming skills are distinct.

Print a string of $ n $ characters; $ i $ -th character should be 1 if $ i $ -th student joins the first team, or 2 otherwise.

5 2
2 4 5 3 1

11111

5 1
2 1 3 5 4

22111

7 1
7 2 1 3 5 4 6

1121122

5 1
2 4 5 3 1

21112

In the first example the first coach chooses the student on a position $ 3 $ , and the row becomes empty (all students join the first team). In the second example the first coach chooses the student on position $ 4 $ , and the row becomes $ [2, 1] $ (students with programming skills $ [3, 4, 5] $ join the first team). Then the second coach chooses the student on position $ 1 $ , and the row becomes empty (and students with programming skills $ [1, 2] $ join the second team). In the third example the first coach chooses the student on position $ 1 $ , and the row becomes $ [1, 3, 5, 4, 6] $ (students with programming skills $ [2, 7] $ join the first team). Then the second coach chooses the student on position $ 5 $ , and the row becomes $ [1, 3, 5] $ (students with programming skills $ [4, 6] $ join the second team). Then the first coach chooses the student on position $ 3 $ , and the row becomes $ [1] $ (students with programming skills $ [3, 5] $ join the first team). And then the second coach chooses the remaining student (and the student with programming skill $ 1 $ joins the second team). In the fourth example the first coach chooses the student on position $ 3 $ , and the row becomes $ [2, 1] $ (students with programming skills $ [3, 4, 5] $ join the first team). Then the second coach chooses the student on position $ 1 $ , and the row becomes empty (and students with programming skills $ [1, 2] $ join the second team).