## JOI '14 Open P6 - Secret

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Points: 17 (partial)
Time limit: 9.0s
Memory limit: 512M

Problem type
Allowed languages
C, C++
##### Contest Day 2 - JOI Open Contest

Anna invented a secret binary operation . For non-negative integers , less than or equal to , a non-negative integer less than or equal to is determined. This operation is associative. Namely, the equality holds for non-negative integers , , less than or equal to . This value is simply denoted by .

Anna planned to play a game with Bruno. She asked him to guess the operation . She showed integers to him. She gave to him a number of queries of the following form: "What is the value of ?"

Bruno said it is difficult to play this game without hints. Anna decided to give hints to him. Each hint is given as follows: he will choose , to ask the value of , and she will tell him the value of . He can ask for hints when the integers are given in the beginning of the game. He can also ask for hints when she gives a query to him. Of course, he would like to reduce the number of hints. Because he would like to behave as if he knows almost everything about the operation , he would especially like to reduce the number of hints after a query is given to him.

Write a program which implements Bruno's strategy to ask for hints and answer Anna's queries correctly.

#### Implementation Details

You should write a program which implements the strategy to ask for hints and answer Anna's queries. Your program should include the header file secret.h by #include "secret.h"

Your program should implement the following procedures.

• void Init(int N, int A[])


This procedure is called only once in the beginning. The parameter is the number of the integers shown by Anna. The parameter is an array of length . The elements are the integers shown by her.

• int Query(int L, int R)


This procedure is called when Anna gives a query to Bruno. This means she is asking the value of  .

The following procedure can be called by your program.

• int Secret(int X, int Y)

This procedure is called when Bruno asks for a hint. This means he is asking about the value of . The parameters and should be integers satisfying and . If this procedure is called with parameters not satisfying this condition, your program is considered as Wrong Answer  and terminated.

This procedure returns the value of .

#### Constraints

All input data satisfy the following conditions.

• .
•  .
• The number of calls to Query is less than or equal to .

The score will be given to your program if your program terminates successfully for each test case, it is not considered as Wrong Answer , and it returns the correct value for each call to Query.

Your score is calculated as follows.

1. Your score is if the following two conditions are satisfied for each test case:
• In Init, the number of calls to Secret is less than or equal to .
• In each call to Query, the number of calls to Secret is less than or equal to .
2. Your score is if your program does not satisfy (1), and the following two conditions are satisfied:
• In Init, the number of calls to Secret is less than or equal to .
• In each call to Query, the number of calls to Secret is less than or equal to .
3. Your score is if your program does not satisfy (1) or (2).