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Bakery Survey This is an interactive problem. Your city has n bakeries (where n is a power of 2), and bakery i specializes in one type of cake a_i. You want to determine d — the number of distinct cake types available in the city. You don't know the values of a_1, ..., a_n. However, your friend can help you by tasting cakes. Your friend has a memory capacity of k (where k is also a power of 2), which works as follows: Your friend's memory is a queue S. You can perform two types of operations: 1. Query operation: Ask your friend to taste the cake from bakery c. This will: - Tell you whether a_c is already in S (the last k cake types tasted) - Add a_c to the end of S - If |S| > k, remove the front element from S 2. Reset operation: Clear your friend's memory, making S empty. Your goal is to find d while minimizing the total cost of operations. This problem is graded based on the total cost of operations. The cost is calculated as: Total Cost = (number of resets) × n + (number of queries) + 1 Your answer will be compared to a reference solution ref_cost. Your final score will be calculated as the average of 100 × min(ref_cost / your_cost, 1) across all test cases. You must use at most 100,000 operations in total. Input The first line contains two integers n and k (1 ≤ k ≤ n ≤ 1024, both k and n are powers of 2). Interaction To perform an operation, output one line in one of the following formats: ? c — Ask your friend to taste the cake from bakery c (1 ≤ c ≤ n). R — Reset your friend's memory. After a query operation, read a single character: - Y (Yes) if a_c is in the memory S - N (No) if a_c is not in the memory S When you have found the answer, output: ! d — where d is the number of distinct cake types. After printing the answer, your program should terminate immediately. To flush your output, use: - fflush(stdout) or cout.flush() in C++ - System.out.flush() in Java - stdout.flush() in Python Example Input: 4 2 N N Y N N N N Output: ? 1 ? 2 ? 3 ? 4 R ? 4 ? 1 ? 2 ! 3 Time limit: 4 seconds Memory limit: 512 MB |