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.

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.

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 $[7, 9]$ .