Big Difference

You are given two integers $N$ and $K$. Find any two integers $a$ and $b$ such that - $1 \leq a, b \leq N$, - $|a - b| \geq K$, and - $|\gcd(a, b) - \text{lcm}(a, b)| \geq 2K$ That is, your task is to find any two integers not exceeding $N$, such that they differ by at least $K$ and their GCD and LCM differ by at least $2K$. It is possible that no valid $(a, b)$ exist, in which case you must pr