Smallest embedded linux distro?

I like to ask to the experts out there… What is the best embedded linux distro for:

Flash memory ~ 700Kb
Ram ~ 256Kb
Processor: High end arm cortex STM32F103C8T6 (something from STM32 family for eg)
Required modules: - Kernel core - Basic driver set: USB/Networking (for WiFi - No AP, just client, no security)/SPI/Uart/I2C

Is this at all possible or am I dreaming?

The idea is to use a 5$ high end CortexM3 and don’t use any external memories so that I can enjoy the ready drivers for SDIO/WiFi etc.

I updated the question with clarification on WiFi. WiFi in the sense that it is a simple, run of the mill client. Nothing fancy, perhaps wep if I can fit it.
Another update: How about uCLinux?

If you don’t need access to GPU there’s a lot you can do. The existing kernel can probably be used with any user space rootfs. It would still be a difficult job, and I’m not sure if a TK1 is practical when you’ve given up the part that makes it really shine. You could get GPU back in if you installed the existing X server (you don’t need to run a graphical desktop, but you need this to interface with the driver).