R - output overlapping intervals

fileA contains intervals (start, end), and a value assigned to that interval (value).

start     end      value
0         123      1      #value 1 at positions 0 to 122 included.
123       78000    0      #value 0 at positions 123 to 77999 included.
78000     78004    56     #value 56 at positions 78000, 78001, 78002 and 78003.
78004     78005    12     #value 12 at position 78004.
78005     78006    1      #value 1 at position 78005.
78006     78008    21     #value 21 at positions 78006 and 78007.
78008     78056    8      #value 8 at positions 78008 to 78055 included.
78056     81000    0      #value 0 at positions 78056 to 80999 included.

fileB contains a list of the intervals I am interested in. I would like to retrieve the overlapping intervals from fileA. The starts and ends do not necessarily match. Here is an example of fileB:

start     end      label
77998     78005    romeo
78007     78012    juliet

The goal is to (1) retrieve the intervals from fileA that overlap with fileB and (2) to append the corresponding labels from fileB. The expected result is (# to designate the lines that were discarded, this is to help visualize and will not be in the final output):

start     end      value    label
#
123       78000    0        romeo
78000     78004    56       romeo
78004     78005    12       romeo
#
78006     78008    21       juliet
78008     78056    8        juliet
#

Here is my attempt at writing code:

#read from tab-delimited text files which do not contain column names
A<-read.table("fileA.txt",sep="\t",colClasses=c("numeric","numeric","numeric"))
B<-read.table("fileB.txt",sep="\t",colClasses=c("numeric","numeric","character"))

#add column names
colnames(A)<-c("start","end","value")
colnames(B)<-c("start","end","label")

#output intervals in `fileA` that overlap with an interval in `fileB`
A_overlaps<-A[((A$start <= B$start & A$end >= B$start)
              |(A$start >= B$start & A$start <= B$end)
              |(A$end >= B$start & A$end <= B$end)),]

At this point I am already getting unexpected results:

> A_overlaps
  start   end value
  #missing
3 78000 78004    56
5 78005 78006     1   #this line should not be here
6 78006 78008    21
  #missing

I didn't write the part to output the labels yet because I might as well fix this first, but I can't figure out what I am getting wrong...

[EDIT] I also tried the following but it just outputs the entirety of fileA:

A_overlaps <- A[(min(A$start,A$end) < max(B$start,B$end)
               & max(A$start,A$end) > min(B$start,B$end)),]

This produces desired output, but may be a little difficult to read

# function to find, if value lies in interval
is.between <- function(x, a, b) {
  (x - a)  *  (b - x) > 0
}

# apply to all rows in A 
> matching <- apply(A, MARGIN=1, FUN=function(x){
# which row fulfill following condition:
+   which(apply(B, MARGIN=1, FUN=function(y){
# first value lies in interval from B or second value lies in interval from B
+     is.between(as.numeric(x[1]), as.numeric(y[1]), as.numeric(y[2])) | is.between(as.numeric(x[2]), as.numeric(y[1]), as.numeric(y[2]))
+     }))
+   })
> 
# print the results
> matching
[[1]]
integer(0)

[[2]]
[1] 1

[[3]]
[1] 1

[[4]]
[1] 1

[[5]]
integer(0)

[[6]]
[1] 2

[[7]]
[1] 2

[[8]]
integer(0)

> 
# filter those, which has 0 length = no matching
> A_overlaps <- A[unlist(lapply(matching, FUN=function(x)length(x)>0)),]
# add label
> A_overlaps$label <- B$label[unlist(matching)]
> 
> A_overlaps
  start   end value  label
2   123 78000     0  romeo
3 78000 78004    56  romeo
4 78004 78005    12  romeo
6 78006 78008    21 juliet
7 78008 78056     8 juliet