Logo for online store

I need the logo of the online store akademiazabawek.pl. We have a concept for the look of this logo, it should be properly adjusted (unless the client will have a better vision and show the prototype that we accept) - we provide it in the attachment.

The genesis of our logo concept - akademiazabawek.pl store offers toys for children, but at the same time we will be describing toys from a little scientific point of view (detailing the skills that toys develop, study them, etc.). That's why the idea appeared that the logo was a block that would also look like a student cap - with reference to the word "academy" and a more scientific approach.

The colors are also not accidental - blue is supposed to symbolize knowledge and experience, the yellow inset is supposed to refer to the fun and joy of children.

The logo should be prepared in such a way that it looks good as a small picture (eg on a smartphone) as well as in black and white print. In addition, the logo should be possible for horizontal and vertical presentation along with the store name. Modern styles are preferred - flat, subway etc. (generally - simple colors, without significant gradients). The logo itself is to be prepared (without the inscription "Akademia Zabawek").

As part of the order, the contractor is to prepare a vector file in any graphics program that will be forwarded to the client (or you will need to convert the file to a more popular format).