Moving cursor to end of line when using history-search-backward

I recently added the following lines to my .inputrc:

"\e[A": history-search-backward
"\e[B": history-search-forward

However, I noticed when using this that my cursor does not jump to the end of the line. For example, if I type ls then hit up, my terminal will look like this (| being the cursors):

ls |verylongdir

What I want is:

ls verylongdir|

I believe zsh behaves this way with the same command. Is there any way to do this in bash?