Why do you need to render a scene at that high resolution?
When making an image larger (print size) the view distance is usually further away. So the DPI should be dictated by what the eye can see. One rarely goes up really close to a huge poster. And if so one does not expect to see infinite detail in the image.
I typically use 75 dpi for large prints, then interpolate them in PS for the print just to smooth out the pixles.
Or in rare cases use 130 dpi if I want high fidelity.
1225 mm = 48.2"
48.2" @ 75dpi = 3615 px
48.2" @ 130 dpi = 6266 px
And I’ll explain why:
This is the HD vs UHD calculation chart:
Figure out the field of view fill rate for you image.
If your typical view distance is 1 meter for such an image then your field of view will be 62 degrees.
The THX recommendation for TV’s are 30’ fillrate for FullHD, which gives you is around 64 pixles per degree.
4K is recommended for Movie use, where one wants a more immense experience thus the field of view fillrate is higher, close to 90 degrees. (4000 divided by 90 degrees = 44 pixels pr angle)
So lets use 100 pixels per angle to be really sure the image will look great even when users move in to 50 cm view distance:
62 degrees x 100 = 6200x6200 pixles.
Most printers will not show any difference between a 200 dpi and a 300 dpi image, even up really close, at least not for images, and especially if they are interpolated prior to printing. Just do a test for your self:
Print an image from Photoshop at 300 dpi, then downsample to 150 dpi and print, no resample to 300 dpi and print.
Then do the same viewing evaluation at your desired distance.