have to, had to还是be going to have to

问题描述

辅导班一道题：
用 must / have to / had to / mustn't / needn't 填空：
We didn't have any food yesterday, so we _______ go shopping.
老师给的答案是 have to。我认为 so we _______ go shopping 未给出时间，应该一般现在时 have to（现在去买）、过去时had to（昨天买）、将来时 are going to have to（准备去买）都对，请专家指教，谢谢！

老师答疑

黎老师：