24758번 - RSA Mistake 다국어

An RSA number is a positive integer $n$ that is the product of two distinct primes. For example, $10 = 2 \cdot 5$ and $77 = 7 \cdot 11$ are RSA numbers whereas $7 = 7, 9 = 3 \cdot 3$, and $105 = 3 \cdot 5 \cdot 7$ are not.

You are teaching a course that covers RSA cryptography. For one assignment problem, you asked students to generate RSA numbers. They were to submit two positive integers $A, B$. Ideally, these would be distinct prime numbers. But some students submitted incorrect solutions. If they were not distinct primes, partial credit can be earned if $A \cdot B$ is not an integer multiple of $k^2$ for any integer $k \geq 2$. If there is an integer $k \geq 2$ such that $k^2$ divides $A \cdot B$, then the student receives no credit.

For a pair of positive integers submitted by a student for the assignment, determine if they should receive full credit, partial credit, or no credit for this submission.

Note: In the sixth sample case below, the number $545\,528\,636\,581 \cdot 876\,571\,629\,707$ is divisible by $1\,000\,003^2$ and in the seventh sample case below, the number $431\,348\,146\,441 \cdot 3$ is divisible by $656\,771^2$.

The input consists of a single line containing two integers $A$ ($2 \leq A \leq 10^{12}$) and $B$ ($2 \leq B \leq 10^{12}$), which are the two submitted numbers.

Display if the student should receive full credit, partial credit, or no credit for the submitted numbers.