Create a single tall image from a multi-page pdf file

Question

I would like to take a multi-pake pdf file, and have all of the pages "appended" from top to bottom edge to create a single tall image. I am a teacher, and I currently do this by hand, I am then able to annotate the entire page and croll down an entire document inside of Photoshop.
Here is an example: I have a pdf with 4 pages. Currently I open the pdf in PS, I end up with 4 images; I adjust the vertical canvas size of one of the images to be 4 times it's original size, then one-by-one I copy the contents of each image to that new tall image and move that layer vertically below the previous one. So the result is say a 1024x6400 pixel image.
I would like to be able to just open the pdf with a script and get this all done in one step.
Any help is appreciated.

Answer 1

Thanks again c.pfaffenbichler. I had most of it worked out in my own way before you got back to me, but I wasn't able to get the final naming part down.
Like I said, I am a math teacher, and I use photoshop as my whiteboard, and draw with a graphics tablet. So I can print to pdf from any program, now I can import any document into photoshop basically to write on it. So this is wonderful. I have never seen another teacher use PS as a whiteboard in class in this way, so I am most likely the only person in my county or state that would need such a script.
After I got everything worked out, I added some things to the script. Some of my colleagues will use my files as a whiteboard if I send it to them as a tall single page pdf that they can scroll down and write over; so they don't need photoshop. So I have scripted in the saving of that pdf as well. Here are my changes; most of what I changed is in the section commented MY WORK.
// opens all pages of pdfs cropped to trimbox with set settings and arranges them;
// 2011, use it at your own risk;
#target photoshop
// dialog for pdf-selection;
var theFiles = app.openDialog();
if (theFiles) {
     for (var m = 0; m < theFiles.length; m++) {
          var theFile = theFiles[m];
          if (theFile.name.slice(-4) == ".pdf") {
               var thePdf = openMultipagePDF(theFile);
          else {alert (theFile.name + " is not a pdf-file")}
////// function to open all pages of a pdf //////
////// influenced by PlaceMultipagePDF.jsx //////
function openMultipagePDF(myPDFFile) {
// pdf open options;
     var pdfOpenOpts = new PDFOpenOptions;
     pdfOpenOpts.antiAlias = true;
     pdfOpenOpts.bitsPerChannel = BitsPerChannelType.EIGHT;
     pdfOpenOpts.cropPage = CropToType.MEDIABOX;
     pdfOpenOpts.mode = OpenDocumentMode.RGB;
     pdfOpenOpts.resolution = 247.8;
     pdfOpenOpts.suppressWarnings = true;
     pdfOpenOpts.usePageNumber  = true;
// change pref;
     var originalRulerUnits = app.preferences.rulerUnits;
     app.preferences.rulerUnits = Units.PIXELS;
// suppress dialogs;
     var theDialogSettings = app.displayDialogs;
     app.displayDialogs = DialogModes.NO;
// iterate through pages until fail;
          var myCounter = 1;
          var myBreak = false;
          var theWidth = 0;
          var theHeight = 0;
          while(myBreak == false){
               pdfOpenOpts.page = myCounter;
               try {
                    var thePdf = app.open(myPDFFile, pdfOpenOpts);
                    if (thePdf.width > theWidth) {theWidth = thePdf.width};
                    var offset = thePdf.height;
                    thePdf.layers[0].name = myPDFFile.name+"_"+myCounter;
                    if (myCounter == 1) {
                         var theFile = thePdf
                    else {
                         thePdf.layers[0].duplicate(theFile, ElementPlacement.PLACEATBEGINNING);
                         thePdf.close(SaveOptions.DONOTSAVECHANGES)
                    myCounter = myCounter + 1;
                    var theLayer = app.activeDocument.activeLayer;
                    theLayer.translate(0, theHeight);
                    theHeight = theHeight + offset;
            catch (e) {myBreak = true};
// reset dialogmodes;
app.displayDialogs = DialogModes.ERROR;
app.preferences.rulerUnits = originalRulerUnits;
// resize canvas;
    theFile.resizeCanvas(theWidth, theHeight, AnchorPosition.TOPLEFT);
//MY WORK
// merge visible layers (even if there is only one layer)
     try     {
          theFile.mergeVisibleLayers();
          }catch(e) {}
// create layer, rename, movetobottom, fill white
     theFile.artLayers.add();
     theFile.layers[0].name = "Background";
     theFile.layers[0].move(theFile.layers[1], ElementPlacement.PLACEAFTER);
     var white = new SolidColor();
     white.rgb["hexValue"] = "ffffff";
     theFile.selection.selectAll();
     theFile.selection.fill(white);
//rename contents layer, add "work" layer for teacher to write on
     theFile.layers[0].name = "Problems";
     theFile.artLayers.add();
     theFile.layers[0].name = "Work";
//force 2107 width
//     if(theFile.width != 2107) theFile.resizeImage(UnitValue(2107, "px"), undefined, undefined, ResampleMethod.BICUBIC);
// force 2048 width
     if(theFile.width != 2048) theFile.resizeImage(UnitValue(2048, "px"), undefined, undefined, ResampleMethod.BICUBIC);
// save psd;
    psdOpts = new PhotoshopSaveOptions();
    psdOpts.embedColorProfile = true;
    psdOpts.alphaChannels = false;
    psdOpts.layers = true;
    psdOpts.maximizeCompatibility = true;
    var filePathPsd = myPDFFile.path+"/"+myPDFFile.name.slice(0, -4)+".psd";
    if (filePathPsd.exists) filePathPsd.remove();
    theFile.saveAs(File(filePathPsd), psdOpts, false)
// save pdf whiteboard
    var pdfOpts = new PDFSaveOptions;
    pdfOpts.downSample = PDFResample.NONE;
    pdfOpts.optimizeForWeb = true;
    pdfOpts.PDFCompatibility = PDFCompatibility.PDF15;
    pdfOpts.preserveEditing = false;
    pdfOpts.encoding = PDFEncoding.PDFZIP;
    var filePathPdf = myPDFFile.path+"/"+myPDFFile.name.slice(0, -4)+" Whiteboard.pdf";
    if (filePathPdf.exists) filePathPdf.remove();
    theFile.saveAs(File(filePathPdf), pdfOpts, false)
    theFile.close(SaveOptions.DONOTSAVECHANGES)
//MY WORK
     return theFile