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internbootcamp/bootcamp/cprimitiveprimes/cprimitiveprimes.py

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+"""# 
+
+### 谜题描述
+It is Professor R's last class of his teaching career. Every time Professor R taught a class, he gave a special problem for the students to solve. You being his favourite student, put your heart into solving it one last time.
+
+You are given two polynomials f(x) = a_0 + a_1x + ... + a_{n-1}x^{n-1} and g(x) = b_0 + b_1x + ... + b_{m-1}x^{m-1}, with positive integral coefficients. It is guaranteed that the cumulative GCD of the coefficients is equal to 1 for both the given polynomials. In other words, gcd(a_0, a_1, ..., a_{n-1}) = gcd(b_0, b_1, ..., b_{m-1}) = 1. Let h(x) = f(x)⋅ g(x). Suppose that h(x) = c_0 + c_1x + ... + c_{n+m-2}x^{n+m-2}. 
+
+You are also given a prime number p. Professor R challenges you to find any t such that c_t isn't divisible by p. He guarantees you that under these conditions such t always exists. If there are several such t, output any of them.
+
+As the input is quite large, please use fast input reading methods.
+
+Input
+
+The first line of the input contains three integers, n, m and p (1 ≤ n, m ≤ 10^6, 2 ≤ p ≤ 10^9), — n and m are the number of terms in f(x) and g(x) respectively (one more than the degrees of the respective polynomials) and p is the given prime number.
+
+It is guaranteed that p is prime.
+
+The second line contains n integers a_0, a_1, ..., a_{n-1} (1 ≤ a_{i} ≤ 10^{9}) — a_i is the coefficient of x^{i} in f(x).
+
+The third line contains m integers b_0, b_1, ..., b_{m-1} (1 ≤ b_{i} ≤ 10^{9}) — b_i is the coefficient of x^{i} in g(x).
+
+Output
+
+Print a single integer t (0≤ t ≤ n+m-2) — the appropriate power of x in h(x) whose coefficient isn't divisible by the given prime p. If there are multiple powers of x that satisfy the condition, print any.
+
+Examples
+
+Input
+
+
+3 2 2
+1 1 2
+2 1
+
+
+Output
+
+
+1
+
+
+Input
+
+
+2 2 999999937
+2 1
+3 1
+
+
+Output
+
+
+2
+
+Note
+
+In the first test case, f(x) is 2x^2 + x + 1 and g(x) is x + 2, their product h(x) being 2x^3 + 5x^2 + 3x + 2, so the answer can be 1 or 2 as both 3 and 5 aren't divisible by 2.
+
+In the second test case, f(x) is x + 2 and g(x) is x + 3, their product h(x) being x^2 + 5x + 6, so the answer can be any of the powers as no coefficient is divisible by the given prime.
+
+Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
+```python
+n,m,p=map(int,raw_input().strip().split())
+a=map(int,raw_input().strip().split())
+b=map(int,raw_input().strip().split())
+ans=0
+for i in xrange(n):
+    if a[i]%p!=0:
+        ans+=i
+        break
+for i in xrange(m):
+    if b[i]%p!=0:
+        ans+=i
+        break
+print ans
+```
+
+
+请完成上述谜题的训练场环境类实现，包括所有必要的方法。
+"""
+
+from bootcamp import Basebootcamp
+from bootcamp import Basebootcamp
+import re
+import random
+import math
+
+class Cprimitiveprimesbootcamp(Basebootcamp):
+    def __init__(self, max_n=5, max_m=5, primes=None, **params):
+        super().__init__(**params)
+        self.max_n = max_n
+        self.max_m = max_m
+        self.primes = primes or [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
+    
+    def case_generator(self):
+        while True:
+            n = random.randint(1, self.max_n)
+            m = random.randint(1, self.max_m)
+            p = random.choice(self.primes)
+            
+            # Ensure first non-divisible index exists
+            k_a = random.randint(0, n-1)
+            k_b = random.randint(0, m-1)
+
+            # Generate a-coefficients
+            a = []
+            valid_a = False
+            for i in range(n):
+                if i < k_a or i > k_a:
+                    a_val = p  # Ensure other coefficients are multiples of p
+                else:
+                    a_val = random.randint(1, 10)
+                    while a_val % p == 0:
+                        a_val = random.randint(1, 10)
+                a.append(a_val)
+            
+            # Check GCD for a
+            gcd_a = a[0]
+            for num in a[1:]:
+                gcd_a = math.gcd(gcd_a, num)
+                if gcd_a == 1:
+                    break
+            if gcd_a != 1:
+                continue
+            
+            # Generate b-coefficients
+            b = []
+            for j in range(m):
+                if j < k_b or j > k_b:
+                    b_val = p  # Ensure other coefficients are multiples of p
+                else:
+                    b_val = random.randint(1, 10)
+                    while b_val % p == 0:
+                        b_val = random.randint(1, 10)
+                b.append(b_val)
+            
+            # Check GCD for b
+            gcd_b = b[0]
+            for num in b[1:]:
+                gcd_b = math.gcd(gcd_b, num)
+                if gcd_b == 1:
+                    break
+            if gcd_b != 1:
+                continue
+            
+            return {
+                'n': n,
+                'm': m,
+                'p': p,
+                'a': a,
+                'b': b
+            }
+    
+    @staticmethod
+    def prompt_func(question_case):
+        a_coeffs = ', '.join(map(str, question_case['a']))
+        b_coeffs = ', '.join(map(str, question_case['b']))
+        prompt = f"""It is Professor R's last class of his teaching career. Every time Professor R taught a class, he gave a special problem for the students to solve. You, being his favorite student, put your heart into solving it one last time.
+
+You are given two polynomials f(x) and g(x) with positive integral coefficients. The cumulative GCD of the coefficients of each polynomial is 1. You are also given a prime number p. Your task is to find any exponent t in the product polynomial h(x) = f(x)⋅g(x) such that the coefficient of x^t, c_t, is not divisible by p. If there are multiple such t, output any of them.
+
+Input format:
+- The first line contains three integers n, m, p: the number of terms in f(x), g(x), and the prime number p respectively.
+- The second line contains n integers a_0, a_1, ..., a_{{n-1}} — the coefficients of f(x).
+- The third line contains m integers b_0, b_1, ..., b_{{m-1}} — the coefficients of g(x).
+
+Input values for this problem:
+n = {question_case['n']}, m = {question_case['m']}, p = {question_case['p']}
+a coefficients: {a_coeffs}
+b coefficients: {b_coeffs}
+
+Please determine the appropriate value of t and output it. Place your final answer within [answer] and [/answer] tags. For example, if your answer is 3, write [answer]3[/answer]."""
+        return prompt
+    
+    @staticmethod
+    def extract_output(output):
+        matches = re.findall(r'\[answer\](.*?)\[/answer\]', output, re.IGNORECASE)
+        if not matches:
+            return None
+        return matches[-1].strip()
+    
+    @classmethod
+    def _verify_correction(cls, solution, identity):
+        try:
+            t = int(solution)
+        except:
+            return False
+        
+        p = identity['p']
+        a = identity['a']
+        b = identity['b']
+        
+        # Find first non-divisible index in a
+        i = next((idx for idx, coeff in enumerate(a) if coeff % p != 0), None)
+        # Find first non-divisible index in b
+        j = next((idx for idx, coeff in enumerate(b) if coeff % p != 0), None)
+        
+        return t == i + j