check this out :
had to in affirmative sentences (Simple Past)
Example:
I/you/he/she/it/we/you/they had to get up early.
had to in negative sentences (Simple Past)
Example:
I/you/he/she/it/we/you/they did not have to get up early
contracted forms:
I/you/he/she/it/we/you/they didn't have to get up early.
to sum up it seams when you want answer in negative form(no matter whether it's in affirmative or negative sentence) you can say that with did ....