F. Katya and Segments Setstime limit per test3.5 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputIt 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.InputThe 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.OutputFor each query, print "yes" or "no" in a new line.InteractionAfter 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.ExampleInput
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
Output
no
yes
yes
no
yes
NoteFor 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].
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 
['data structures', 'interactive', 'sortings', '*2400']