Awk - join multiple files

Is it possible to join all the files with input1 based on 1st column?

input1

a
b
c
d
e
f

input2

a
b

input3

a
e

input4

c
d
e
f

inputx

a
awk -f join.awk input1 input2 input3 input4 inputx .....

output

a  4  input1  input2  input3  inputx
b  2  input1  input2  0  0  0
c  2  input1  0  0  input4  0
d  2  input1  0  0  input4  0
e  3  input1  0  input3  input4  0
f  2  input1  0  0  input4  0

note: 2nd column represents how many times the symbol appeared in x nummber of inputs

$ cat join.awk
{
 totalcnt[$1]++
 if(FILENAME != prevfilename)
  filesc++
 filecnt[filesc,$1]++
 fname[filesc]=prevfilename=FILENAME
}

END {
 for(i in totalcnt)
 {
  printf("%s\t%s",i,totalcnt)
  for(j=1;j<=filesc;j++)
  {
   printf("\t%s[%d]",fname[j],filecnt[j,i])
  }
  printf("%s","\n");
 }
}

Slight mod to elixir_sinari's post to match OP request for filenames not count:

$ cat join.awk
{
 totalcnt[$1]++
 filesc+=(FNR==1)
 filecnt[filesc,$1]=FILENAME
}
END {
 OFS="\t"
 for(i in totalcnt) {
  $0=""; $1=i; $2=totalcnt
  for(j=1;j<=filesc;j++)
     $(j+2)=filecnt[j,i]?filecnt[j,i]:"0"
  print
 }
}