Need help with cylindrical material

I need a material for a cylinder with rings of icons. The cylinder only has the walls and will have three rings, each with a tiled icon around it. The icons are square, which helps. I have the cylinder UV set for 1-0 and a base material with Mask-G->Multiply*3->Floor->IF node comparing to 1 with A<B being first ring, A=B, for second, and A>B for third ring. I am trying with only base textures to test instead of atlas, but I cannot seem to get the icons to tile only in the single band cleanly.