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] $ .