Katya and Segments Sets
Description
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.
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.
For each query, print "yes" or "no" in a new line.
Interaction
After printing a query, do not forget to output end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use:
- fflush(stdout) or cout.flush() in C++;
- System.out.flush() in Java;
- flush(output) in Pascal;
- stdout.flush() in Python;
- see documentation for other languages.
Input
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.
Output
For each query, print "yes" or "no" in a new line.
Samples
5 5 9
3 6 3
1 3 1
2 4 2
1 2 3
4 6 5
2 5 3
7 9 4
2 3 1
4 10 4
1 2 2 3
1 2 2 4
1 3 1 5
2 3 3 6
2 4 2 9
no
yes
yes
no
yes
Note
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 $[7, 9]$.