Kuroni the Private Tutor

题面翻译

题目描述

Kuroni 举行了一场考试，有 $n$ 道试题， $m$ 位学生参加的考试，每一题的分值为 1 分。第 $i$ 个问题至少有 $l_i$ 人答对，最多有 $r_i$ 人答对。此外，你还知道所有学生的总成绩为 $t$ 。

你浏览了考试的最终排名，学生的排名从 1 到 $m$ ，第 1 名的学生得分最高，第 $m$ 名的学生得分最低。

同时，你知道排名 $p_i$ 的学生的得分为 $s_i$ 。

Kuroni 希望你回答：

• 最多能有多少人并列第一；
• 在有尽量多的人并列第一的情况下，第一名的分数最高是多少。

输入格式

第一行两个整数 $n$ ,$m$ 。

接下来 $n$ 行，每行两个整数，表示 $l_i$ 和 $r_i$ 。

下面一行一个整数 $q$ 。

接下来 $q$ 行，每行两个整数，表示 $p_i$ 和 $s_i$ 。

最后一行一个整数 $t$ 。

所有变量的意义同题目描述。

输出格式

一行两个整数，为所求答案，如果无解，请输出 -1 -1 。

数据范围

$1 \le n$ , $m \le 10^5$

$0 \le l_i \le r_i \le m$

$0 \le q \le m$

$1 \le p_i \le m$ , $0 \le s_i \le n$

$0 \le t \le nm$

题目描述

As a professional private tutor, Kuroni has to gather statistics of an exam. Kuroni has appointed you to complete this important task. You must not disappoint him.

The exam consists of $n$ questions, and $m$ students have taken the exam. Each question was worth $1$ point. Question $i$ was solved by at least $l_i$ and at most $r_i$ students. Additionally, you know that the total score of all students is $t$ .

Furthermore, you took a glance at the final ranklist of the quiz. The students were ranked from $1$ to $m$ , where rank $1$ has the highest score and rank $m$ has the lowest score. Ties were broken arbitrarily.

You know that the student at rank $p_i$ had a score of $s_i$ for $1 \le i \le q$ .

You wonder if there could have been a huge tie for first place. Help Kuroni determine the maximum number of students who could have gotten as many points as the student with rank $1$ , and the maximum possible score for rank $1$ achieving this maximum number of students.

输入格式

The first line of input contains two integers ( $1 \le n, m \le 10^{5}$ ), denoting the number of questions of the exam and the number of students respectively.

The next $n$ lines contain two integers each, with the $i$ -th line containing $l_{i}$ and $r_{i}$ ( $0 \le l_{i} \le r_{i} \le m$ ).

The next line contains a single integer $q$ ( $0 \le q \le m$ ).

The next $q$ lines contain two integers each, denoting $p_{i}$ and $s_{i}$ ( $1 \le p_{i} \le m$ , $0 \le s_{i} \le n$ ). It is guaranteed that all $p_{i}$ are distinct and if $p_{i} \le p_{j}$ , then $s_{i} \ge s_{j}$ .

The last line contains a single integer $t$ ( $0 \le t \le nm$ ), denoting the total score of all students.

输出格式

Output two integers: the maximum number of students who could have gotten as many points as the student with rank $1$ , and the maximum possible score for rank $1$ achieving this maximum number of students. If there is no valid arrangement that fits the given data, output $-1$ $-1$ .

样例 #1

样例输入 #1

5 4
2 4
2 3
1 1
0 1
0 0
1
4 1
7

样例输出 #1

3 2

样例 #2

样例输入 #2

5 6
0 6
0 6
2 5
6 6
4 6
1
3 3
30

样例输出 #2

-1 -1

提示

For the first sample, here is one possible arrangement that fits the data:

Students $1$ and $2$ both solved problems $1$ and $2$ .

Student $3$ solved problems $2$ and $3$ .

Student $4$ solved problem $4$ .

The total score of all students is $T = 7$ . Note that the scores of the students are $2$ , $2$ , $2$ and $1$ respectively, which satisfies the condition that the student at rank $4$ gets exactly $1$ point. Finally, $3$ students tied for first with a maximum score of $2$ , and it can be proven that we cannot do better with any other arrangement.