Consider a standard Cartesian coordinate system (the $xy$ plane). A sound source is moving on a parabolic path $\displaystyle{{ y }^{ 2 }=4x}$ with constant speed $\displaystyle{{ v }_{ s }=\cfrac { v }{ 2 } }$. Here $v$ is velocity of sound in still air.

At time $t=0$ the source is at the origin, and an observer is standing at rest at $\displaystyle{(-1,0)}$.
Find the time at which the observer hears the **lowest** frequency he'll hear from the source. The time $T$ can be expressed as
$\displaystyle{T=\cfrac { a\sqrt { b } +c\ln { (\sqrt { d } +e) } }{ v } }$

Find $a+b+c+d+e$ .

**Details**

- Here $a,b,c,d,e$ are positive integers , and $b,d$ are square free integer .