when I want to check my project with the auto test mail and its shows to me (like the attached picture) and I think that the reason is the debug circuit makes error with some inputs because the exponent cant be 0000
what should I do?
As you pointed out, the exponent cannot be 0000. The debug circuit will give an error when fed with 0000, you are correct about that. However, more importantly, if your implementation of gcd yields 0000 as the exponent, it definitely means that your implementation is wrong.