HDU 4569 Special equations(取模)

Posted 2020-07-18 zhaop

Special equations

Time Limit:1000MS     Memory Limit:32768KB     64bit IO Format:%I64d & %I64u

Submit Status Practice HDU 4569

Description

　　Let f(x) = a _nx ⁿ +...+ a ₁x +a ₀, in which a _i (0 <= i <= n) are all known integers. We call f(x) 0 (mod m) congruence equation. If m is a composite, we can factor m into powers of primes and solve every such single equation after which we merge them using the Chinese Reminder Theorem. In this problem, you are asked to solve a much simpler version of such equations, with m to be prime‘s square.

 

Input

　　The first line is the number of equations T, T<=50. 
　　Then comes T lines, each line starts with an integer deg (1<=deg<=4), meaning that f(x)‘s degree is deg. Then follows deg integers, representing a _n to a ₀ (0 < abs(a _n) <= 100; abs(a _i) <= 10000 when deg >= 3, otherwise abs(a _i) <= 100000000, i<n). The last integer is prime pri (pri<=10000). 
　　Remember, your task is to solve f(x) 0 (mod pri*pri)

 

Output

　　For each equation f(x) 0 (mod pri*pri), first output the case number, then output anyone of x if there are many x fitting the equation, else output "No solution!"

 

Sample Input

4

2 1 1 -5 7

1 5 -2995 9929

2 1 -96255532 8930 9811

4 14 5458 7754 4946 -2210 9601

 

Sample Output

Case #1: No solution! Case #2: 599 Case #3: 96255626 Case #4: No solution!