请问王老师一道英语题

If I had remember_____ the window,the thief would not have got in.
填to close 还是closing？
我知道remember to do 是记得去做某件事，但还没做
remembe doing 是记的做过某件事
但是这道题有虚拟语气，我觉得两个都说的过去，而且有的答案选to close,有的答案选closing ,我倾向选closing,请老师告诉我究竟选哪个