Baltic Olympiad in Informatics: 2020 Day 1, Problem 3

Joker returns to Gotham City to execute another evil plan. In Gotham City, there are ~N~ street junctions (numbered from ~1~ to ~N~) and ~M~ streets (numbered from ~1~ to ~M~). Each street connects two distinct junctions, and two junctions are connected by at most one street.

For his evil plan, Joker needs to use an odd number of streets that together form a cycle. That is, for a junction ~S~ and an even positive integer ~k~, there is a sequence of junctions ~S, s_1, \dots, s_k, S~ such that there are streets connecting (a) ~S~ and ~s_1~, (b) ~s_k~ and ~S~, and (c) ~s_{i-1}~ and ~s_i~ for each ~i = 2, \dots, k~.

However, the police are controlling the streets of Gotham City. On each day ~i~, they monitor a different subset of all streets with consecutive numbers ~j~: ~l_i \le j \le r_i~. These monitored streets cannot be a part of Joker's plan, of course. Unfortunately for the police, Joker has spies within the Gotham City Police Department; they tell him which streets are monitored on which day. Now Joker wants to find out, for some given number of days, whether he can execute his evil plan. On such a day there must be a cycle of streets, consisting of an odd number of streets which are not monitored on that day.

Input Specification

The first line of the input contains three integers ~N~, ~M~, and ~Q~ ~(1 \le N, M, Q \le 200\,000)~: the number of junctions, the number of streets, and the number of days to be investigated. The following ~M~ lines describe the streets. The ~j~-th of these lines ~(1 \le j \le M)~ contains two junction numbers ~u~ and ~v~ ~(u \ne v)~, saying that street ~j~ connects these two junctions. It is guaranteed that any two junctions are connected by at most one street. The following ~Q~ lines contain two integers ~l_i~ and ~r_i~, saying that all streets ~j~ with ~l_i \le j \le r_i~ are checked by the police on day ~i~ ~(1 \le i \le Q)~.

Output Specification

Your output is to contain ~Q~ lines. Line ~i~ ~(1 \le i \le Q)~ contains YES if Joker can execute his plan on day ~i~, or NO otherwise.

Scoring

Subtasks:

1. (~6~ points) ~1 \le N, M, Q \le 200~
2. (~8~ points) ~1 \le N, M, Q \le 2\,000~
3. (~25~ points) ~l_i = 1~ for ~i = 1, \dots, Q~
4. (~10~ points) ~l_i \le 200~ for ~i = 1, \dots, Q~
5. (~22~ points) ~Q \le 2\,000~
6. (~29~ points) No further constraints

Sample Input

6 8 2
1 3
1 5
1 6
2 5
2 6
3 4
3 5
5 6
4 8
4 7

Sample Output

NO
YES

Explanation for Sample Output

The graph in the example test: