Reading Books (easy version)
Contest: Codeforces Round 653 (Div. 3)
Difficulty rating: 1600
Tags: data structures, greedy, sortings

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 some amount of 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 some 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 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.

Input format:
The first line of the input contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le k \le n \le 2 \cdot 10^5$$$).

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.

Output format:
If there is no solution, print only one integer -1. Otherwise print one integer $$$T$$$ — the minimum total reading time of the suitable set of books.

Constraints:
Time limit: 2.0 s
Memory limit: 256.0 MB

Example input:
8 4
7 1 1
2 1 1
4 0 1
8 1 1
1 0 1
1 1 1
1 0 1
3 0 0

Example output:
18

Example input:
5 2
6 0 0
9 0 0
1 0 1
2 1 1
5 1 0

Example output:
8

Editorial:
Let's divide all books into four groups:
• 00 — both Alice and Bob doesn't like these books;
• 01 — only Alice likes these books;
• 10 — only Bob likes these books;
• 11 — both ALice and Bob like these books.
Obviously, 00-group is useless now. So, how to solve the problem? Let's iterate over the number of books we take from 11-group. Let it be $$$cnt$$$. Then we obviously need to take exactly $$$k-cnt$$$ books from groups 01 and 10. Among all books in these three groups we have to choose the cheapest ones. To calculate sum of times in each group fast enought, we can sort each group independently and implement prefix sums on these arrays. If $$$k-cnt$$$ is less than zero or greater than the size of 01 or 10-group for each possible $$$cnt$$$ then the answer is -1.
And don't forget that the answer can be up to $$$2 \cdot 10^9$$$.
Time complexity: $$$O(n \log{n})$$$.