Create name-value pair data frame from input with delimiters

I have a data frame which can be created with this code:

input <- data.frame( 'ID'=c(1:3), 
                      Destination=c("AB", "C", "DEF"), 
                      Topic=c("W", "X", "YZ") )

It looks like this:

  ID Destination  Topic
1  1      AB      W
2  2           C      X
3  3 DEF YZ

I would like to create an output data frame that looks like this:

desiredOutput <- data.frame( 
   ID = c(1,1,1,2,2,3,3,3,3,3) , 
   name=c( "Destination", "Destination", "Topic", "Destination", "Topic",
           "Destination", "Destination", "Destination" , "Topic", "Topic"), 
   value=c("A","B", "W", "C", "X", "D", "E", "F", "Y", "Z") )

   ID        name value
1   1 Destination     A
2   1 Destination     B
3   1       Topic     W
4   2 Destination     C
5   2       Topic     X
6   3 Destination     D
7   3 Destination     E
8   3 Destination     F
9   3       Topic     Y
10  3       Topic     Z

Whenever the delimiter occurs, I would like to split the contents into separate rows, with the correct ID, the name of the column, and the corresponding value.

I can split a single column into a list using strsplit, but I don't know how to put the contents into a data frame as above apart from attempting to write a loop. I expect the tidyr package might be helpful.

strsplit(input, split = "")

How can this be done, ideally without a loop?