[Mechanics] Acceleration in the System

I am a high school student and our teacher asked us this question. It is not a homework but he wanted to see if anybody could solve it. The question asks the acceleration of block K with respect to block L. The coefficient of friction is 0, the rope and pulleys are massless. I tried to do an f=ma analysis and then thought that F should be equal to T+ma of block k. However, I am not certain about my last step and I feel like it is wrong. I also tried to provide a constraint condition, taking the second order derivative of the string length, but that made everything worse.

https://preview.redd.it/ue6nhny51j0e1.jpg?width=2074&format=pjpg&auto=webp&s=65ada113917e68e9e93bef51896188e5617b30dc