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F. Katya and Segments Sets
time limit per test
3.5 seconds
memory limit per test
512 megabytes
standard input
standard output

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.


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.
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

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 $$$[7, 9]$$$.