Installing Vinyl (EVP) Flooring (Staircase Question)

I decided to go with Vinyl Planks (EVP) as a replacement to my carpet in my living room area. Its the Corelux Ultra, pretty solid stuff. Anyway, as I am planning how to lay this out I am trying to determine best approach to working around the staircase thats there. Staircase is not being done at the moment, it is also carpet which I plan to pull out and refinish the steps at a later date. So my question is this, I have a post that goes to the ground, and stringer on left side that comes out to ground as well. Do I need to cut the left stringer, bottom riser and post to slip the Vinyl under? Is it permitted to just do a nice cut and have it flush with the steps? I am not a fan of molding all along the bottom of the staircase. I thought I could simply make it flush and caulk or putty the gaps.I know most like the potentially more finished look of it seeming to slip under but if I can start at the stairs and ensure a good fit, any risks there?

I included a picture of the steps, appreciate any feedback you guys may have.

 

Too tight and the floor will buckle as it tries to expand and contract Shoe molding is the way to go. May want to get the flooring under the carpet on the riser and the stringer before adding shoe. With upholstered steps and risers you won't have any pad under or loose carpet. May be prudent to pull back on the carpet on the floor to see what you will be left with after the carpet is removed. The floor will have tack strips and pad. Hopefully this does not leave a gap when you go with the substantially thinner planks.