Correct or not?

"I must leave tomorrow." - He said that he................ leave the following day.

a) must b) had to c) would have to

The model answer is 'c'. I know that 'must' can remain unchanged in reported speech when it is used to express deduction or necessity. Therefore, I think 'a' & 'b' are correct. I think 'would have to' is not a correct choice here. Am I right?