I have no money to take a taxi,so I go home for_____ 是填walk还是walking?为什么?

I have no money to take a taxi,so I go home for_____ 是填walk还是walking?为什么?
I have no money to take a taxi,so I go home for_____ 是填walk还是walking?为什么?

I have no money to take a taxi,so I go home for_____ 是填walk还是walking?为什么?
walking (此时动词walk作介词for的宾语,比较：go for a walk (名词））