Maximize Difference

Chef has two numbers $N$ and $M$. He calls a pair of numbers $(A, B)$ *good* if it satisfies the following conditions: - $1 \le A, B \le M$ - $\gcd(A, B) \ge N$ Chef wants to find a good pair $(A, B)$ such that the value of $|A - B|$ is **maximized**. Can you help Chef? (Here $|X|$ represents the absolute value of $X$). If there are multiple good pairs for which the value of $|A - B|$ is maximiz