Windows app that overrides Print-screen behavior on clipboard

I want a very simple application that will be running on a Windows PC and will be overriding the default behavior of the Print-screen button.
Currently, if you press Print-screen button multiple times while you are doing stuff on your desktop PC, at the end you will only have 1 fullscreen screenshot of your desktop temporarily stored on your clipboard. That happens because every time you press the button, the current contents of the clipboard (e.g. the screenshot from the previous time you pressed the button) get discarded and a new screenshot get stored in the clipboard in its place.

The different thing that I want this application to do is:
if the Print-Screen button is pressed and it finds that the clipboard currently already contains a picture of the same width as the desktop, then it should "stitch" the two pictures (the one already in the clipboard and the current snapshot of the desktop) into one bigger picture that has the same width but bigger the height because the new picture was appended below the existing one.
Please see attached picture for some illustration of the process.

Finally, when you paste the picture (as you would normally do with right-click or Ctrl+V), the clipboard gets emptied. This is default behavior, no change here.

Some final comments:
- if the application is coded in .NET, I'd prefer it. But if the price is low, I'm willing to discuss any language.
- ideally which button press does this whole thing could be a parameter. E.g. instead of Print-Screen, it could be Ctrl+Alt+P. But if it increases the price, I'm fine with Print-Screen