At first I regretted them to stay but we soon became great friends.A. to inviteB. invite

问题补充：

At first I regretted them to stay, but we soon became great friends.

A. to invite

B. invited

C. to have invited

D. inviting

答案：

A. to invite

B. invited

C. to have invited

(答案→)D. inviting

解析：考查非谓语动词。句意：起初，我后悔让他们留下来，但是我们很快成了好朋友。regret doing sth表示后悔做了某事；regret to do sth遗憾（将要）做某事，根据句意可知，invite这个动作已经发生，regret后应该用动名词，排除A、B、C，故选D。