CF1080F.Katya and Segments Sets

It is a very important day for Katya. She has a test in a programming class. As always, she was given an interesting problem that she solved very fast. Can you solve that problem?

You are given $n$ ordered segments sets. Each segment can be represented as a pair of two integers $[l, r]$ where $l\leq r$. Each set can contain an arbitrary number of segments (even $0$). It is possible that some segments are equal.

You are also given $m$ queries, each of them can be represented as four numbers: $a, b, x, y$. For each segment, find out whether it is true that each set $p$ ($a\leq p\leq b$) contains at least one segment $[l, r]$ that lies entirely on the segment $[x, y]$, that is $x\leq l\leq r\leq y$.

Find out the answer to each query.

Note that you need to solve this problem online. That is, you will get a new query only after you print the answer for the previous query.

今天对卡佳来说是非常重要的一天。她正在参加一门编程课的测验。和往常一样，她被给出了一道有趣的题目，并且很快就解决了它。你能解决这道题吗？

你将得到 $n$ 组有序的线段集合。每条线段可表示为一对整数 $[l, r]$，其中 $l \leq r$。每个集合可以包含任意数量的线段（甚至可以为 $0$）。某些线段可能完全相同。

此外，你还得到 $m$ 个查询，每个查询由四个整数 $a, b, x, y$ 表示。对于每个查询，请判断：是否对每个集合 $p$（满足 $a \leq p \leq b$），该集合中都至少存在一条线段 $[l, r]$，使得该线段完全落在区间 $[x, y]$ 内，即满足 $x \leq l \leq r \leq y$。

请依次输出每个查询的答案。

注意：你需要在线解决此问题。也就是说，只有在你输出了前一个查询的答案之后，才会收到下一个查询。

The first line contains three integers $n$, $m$, and $k$ $(1\leq n,m\leq 10^5, 1\leq k\leq 3\cdot10^5)$ — the number of sets, queries, and segments respectively.

Each of the next $k$ lines contains three integers $l$, $r$, and $p$ $(1\leq l\leq r\leq 10^9, 1\leq p\leq n)$ — the limits of the segment and the index of a set, to which this segment belongs.

Each of the next $m$ lines contains four integers $a, b, x, y$ $(1\leq a\leq b\leq n, 1\leq x\leq y\leq 10^9)$ — the description of the query.

第一行包含三个整数 $n$、$m$ 和 $k$（$1\leq n,m\leq 10^5$，$1\leq k\leq 3\cdot10^5$）——分别表示集合的数量、查询的数量以及线段的数量。

接下来的 $k$ 行，每行包含三个整数 $l$、$r$ 和 $p$（$1\leq l\leq r\leq 10^9$，$1\leq p\leq n$）——分别表示该线段的左右端点及其所属集合的编号。

接下来的 $m$ 行，每行包含四个整数 $a$、$b$、$x$、$y$（$1\leq a\leq b\leq n$，$1\leq x\leq y\leq 10^9$）——表示一次查询的描述。

For each query, print "yes" or "no" in a new line.

对于每个查询，在新行中输出 “yes” 或 “no”。

For the first query, the answer is negative since the second set does not contain a segment that lies on the segment $[2, 3]$.

In the second query, the first set contains $[2, 3]$, and the second set contains $[2, 4]$.

In the third query, the first set contains $[2, 3]$, the second set contains $[2, 4]$, and the third set contains $[2, 5]$.

In the fourth query, the second set does not contain a segment that lies on the segment $[3, 6]$.

In the fifth query, the second set contains $[2, 4]$, the third set contains $[2, 5]$, and the fourth contains $[7, 9]$.

对于第一个查询，答案是否定的，因为第二个集合不包含位于线段 $[2, 3]$ 上的任何线段。

在第二个查询中，第一个集合包含 $[2, 3]$，第二个集合包含 $[2, 4]$。

在第三个查询中，第一个集合包含 $[2, 3]$，第二个集合包含 $[2, 4]$，第三个集合包含 $[2, 5]$。

在第四个查询中，第二个集合不包含位于线段 $[3, 6]$ 上的任何线段。

在第五个查询中，第二个集合包含 $[2, 4]$，第三个集合包含 $[2, 5]$，第四个集合包含 $[7, 9]$。