Reading Books (hard version)

做此题前，建议先做 [CF1374E1 Reading Books (easy version)](https://www.luogu.com.cn/problem/CF1374E1) 。 Alice 和 Bob 一共有 $n$ 本书要读。第 $i$ 本书有三个属性：阅读时间 $t_i$ ， $a_i$（为 $1$ 表示 Alice 喜欢这本书，为 $0$ 表示 Alice 不喜欢）， $b_i$ （为 $1$ 表示 Bob 喜欢这本书，为 $0$ 表示 Bob 不喜欢）。 他们需要从这些书中选择 $m$ 本，满足 - 这些书中至少有 $k$ 本是 Alice 喜欢的，至少有 $k$ 本是 Bob 喜欢的。 - 阅读的总时间最小（总时间为选中的书的 $t_i$ 的总和） ### 输入格式 第一行三个整数 $n,m$ 和 $k$ $(1 \leq k \leq n \leq 2 \times 10^5)$ 。 之后的 $n$ 行，每行三个整数 $t_i,a_i,b_i$ $(1 \leq t_i \leq 10^4,0 \leq a_i,b_i \leq 1)$ 。 ### 输出格式 如果无解，输出 ```-1```。 如果有解，第一行输出 $T$ ——最少的阅读时间，第二行输出 $m$ 个不同的数——阅读的书的编号。 e.g. 由于 SPJ ，可以输出任意一种编号的组合，任意一种顺序。

Easy and hard versions are actually different problems, so read statements of both problems completely and carefully. Summer vacation has started so Alice and Bob want to play and joy, but... Their mom doesn't think so. She says that they have to read exactly $ m $ books before all entertainments. Alice and Bob will read each book together to end this exercise faster. There are $ n $ books in the family library. The $ i $ -th book is described by three integers: $ t_i $ — the amount of time Alice and Bob need to spend to read it, $ a_i $ (equals $ 1 $ if Alice likes the $ i $ -th book and $ 0 $ if not), and $ b_i $ (equals $ 1 $ if Bob likes the $ i $ -th book and $ 0 $ if not). So they need to choose exactly $ m $ books from the given $ n $ books in such a way that: - Alice likes at least $ k $ books from the chosen set and Bob likes at least $ k $ books from the chosen set; - the total reading time of these $ m $ books is minimized (they are children and want to play and joy as soon a possible). The set they choose is the same for both Alice an Bob (it's shared between them) and they read all books together, so the total reading time is the sum of $ t_i $ over all books that are in the chosen set. Your task is to help them and find any suitable set of books or determine that it is impossible to find such a set.

The first line of the input contains three integers $ n $ , $ m $ and $ k $ ( $ 1 \le k \le m \le n \le 2 \cdot 10^5 $ ). The next $ n $ lines contain descriptions of books, one description per line: the $ i $ -th line contains three integers $ t_i $ , $ a_i $ and $ b_i $ ( $ 1 \le t_i \le 10^4 $ , $ 0 \le a_i, b_i \le 1 $ ), where: - $ t_i $ — the amount of time required for reading the $ i $ -th book; - $ a_i $ equals $ 1 $ if Alice likes the $ i $ -th book and $ 0 $ otherwise; - $ b_i $ equals $ 1 $ if Bob likes the $ i $ -th book and $ 0 $ otherwise.

If there is no solution, print only one integer -1. If the solution exists, print $ T $ in the first line — the minimum total reading time of the suitable set of books. In the second line print $ m $ distinct integers from $ 1 $ to $ n $ in any order — indices of books which are in the set you found. If there are several answers, print any of them.

6 3 1
6 0 0
11 1 0
9 0 1
21 1 1
10 1 0
8 0 1

24
6 5 1

6 3 2
6 0 0
11 1 0
9 0 1
21 1 1
10 1 0
8 0 1

39
4 6 5