El Professor has a solid plan to heist Royal Mint. Rio needs to hack into its digital security system. Rio chooses a random number between $5$ and $10^{10}$ (both inclusive). Given two numbers $A=94069$ and $B=50549$, the system can be hacked if the number is chosen can be expressed as $Ax+By$, where $x$ and $y$ are non-negative integers. What is the probability Rio hacks into the system?

Report your answer as $\lfloor$ probability $\times 10^{12}$ $\rfloor$, where $\lfloor x \rfloor$ denotes the integer part of $x$.