CF2109C1 Hacking Numbers (Easy Version)

This is the easy version of the problem. In this version, you can send at most $ \mathbf{7} $ commands. You can make hacks only if all versions of the problem are solved. This is an interactive problem. Welcome, Duelists! In this interactive challenge, there is an unknown integer $ x $ ( $ 1 \le x \le 10^9 $ ). You must make it equal to a given integer in the input $ n $ . By harnessing the power of "Mathmech" monsters, you can send a command to do one of the following: CommandConstraintResultCaseUpdateJury's response"add $ y $ " $ -10^{18} \le y \le 10^{18} $ $ \mathrm{res} = x + y $ $ \text{if } 1 \le \mathrm{res} \le 10^{18} $ $ x \leftarrow \mathrm{res} $ "1" $ \mathrm{else} $ $ x \leftarrow x $ "0""mul $ y $ " $ 1 \le y \le 10^{18} $ $ \mathrm{res} = x \cdot y $ $ \text{if } 1 \le \mathrm{res} \le 10^{18} $ $ x \leftarrow \mathrm{res} $ "1" $ \mathrm{else} $ $ x \leftarrow x $ "0""div $ y $ " $ 1 \le y \le 10^{18} $ $ \mathrm{res} = x/y $ $ \text{if } y $ divides $ x $ $ x \leftarrow \mathrm{res} $ "1" $ \mathrm{else} $ $ x \leftarrow x $ "0""digit"— $ \mathrm{res} = S(x) $ $ ^{\text{∗}} $ — $ x \leftarrow \mathrm{res} $ "1"You have to make $ x $ equal to $ n $ using at most $ \mathbf{7} $ commands. $ ^{\text{∗}} $ $ S(n) $ is a function that returns the sum of all the individual digits of a non-negative integer $ n $ . For example, $ S(123) = 1 + 2 + 3 = 6 $

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 5000 $ ). The description of the test cases follows. The first and only line of each test case contains one integer $ n $ ( $ 1 \le n \le 10^9 $ ).

The interaction for each test case begins by reading the integer $ n $ . To send a command, output a line in the following format: - "add $ y $ " Add some integer $ y $ ( $ -10^{18} \le y \le 10^{18} $ ) to $ x $ . The jury will output "1" if $ x + y $ is within $ [1, 10^{18}] $ (successful), and "0" otherwise. If successful, update $ x \leftarrow x + y $ . - "mul $ y $ " Multiply $ x $ by a positive integer $ y $ ( $ 1 \le y \le 10^{18} $ ). The jury will output "1" if $ x \cdot y $ is within $ [1, 10^{18}] $ (successful), and "0" otherwise. If successful, update $ x \leftarrow x \cdot y $ . - "div $ y $ " Divide $ x $ by a positive integer $ y $ ( $ 1 \le y \le 10^{18} $ ). The jury will output "1" if $ y $ is a divisor of $ x $ (successful), and "0" otherwise. If successful, update $ x \leftarrow \frac{x}{y} $ . - "digit" Make $ x $ equal to the sum of its digits. The jury will always output "1" and update $ x \leftarrow S(x) $ . Note that commands are case sensitive. When you have determined that $ x $ is equal to $ n $ , output a line in the following format: - "!" — where the jury will output a "1" if $ n $ is equal to $ x $ , and "-1" otherwise. Note that answering does not count toward your limit of $ \mathbf{7} $ commands. If your program makes more than $ \mathbf{7} $ commands for one test case, or makes an invalid command, then the response to the command will be "-1". After receiving such a response, your program should immediately terminate to receive the verdict Wrong Answer. Otherwise, it may receive any other verdict. After printing a command, do not forget to output the end of the 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; - sys.stdout.flush() in Python; - std::io::stdout().flush() in Rust; - see the documentation for other languages. The interactor is non-adaptive. The unknown integer $ x $ does not change during the interaction. Hacks To hack, use the following format. The first line should contain a single integer $ t $ ( $ 1 \leq t \leq 5000 $ ) — the number of test cases. The first line of each test case should contain two positive integers $ n $ and $ x $ ( $ 1 \leq n,x \leq 10^9 $ ) — denoting the unknown integer and the target value to which it should be made equal, respectively.

SolutionJuryExplanation $ \texttt{2} $ There are 2 test cases. $ \texttt{100} $ In the first test case, the unknown integer $ x = 9 $ and we have to make it equal to $ n = 100 $ . $ \texttt{add -10} $ $ \texttt{0} $ The answer to "add -10" is "0". This means that the addition command was not successful as $ x + y = 9 + (-10) \le 0 $ , and $ x $ remains $ 9 $ after the command $ \texttt{add 1} $ $ \texttt{1} $ The answer to "add 1" is "1". This means that the addition command was successful as $ x + y = 9 + 1 = 10 $ , and $ x $ changes to $ 10 $ after the command. $ \texttt{mul 10} $ $ \texttt{1} $ The answer to "mul 10" is "1". This means that the multiplication command was successful as $ x \cdot y = 10 \cdot 10 = 100 $ , and $ x $ changes to $ 100 $ after the command. $ \texttt{!} $ $ \texttt{1} $ The answer to "!" is "1". This means you have determined that $ x $ equals $ n $ . $ \texttt{5} $ In the second test case, the unknown integer $ x = 1234 $ and we have to make it equal to $ n = 5 $ . $ \texttt{digit} $ $ \texttt{1} $ The answer to "digit" is "1". This means that $ x $ turned into the sum of its digits $ 1 + 2 + 3 + 4 = 10 $ , and $ x $ changes to $ 10 $ after the command. $ \texttt{div 2} $ $ \texttt{1} $ The answer to "div 2" is "1". This means that the division command was successful as $ y = 2 $ is a divisor of $ x = 10 $ , and $ x $ changes to $ \frac{x}{y} = \frac{10}{2} = 5 $ after the command. $ \texttt{!} $ $ \texttt{1} $ The answer to "!" is "1". This means you have determined that $ x $ equals $ n $ .Note that the empty lines in the example input and output are for the sake of clarity, and do not occur in the real interaction.