Given:

$a_1 * (e^{x_1}) + a_2 * (e^{x_2}) + … + a_{30} * (e^{x_{30}}) = 321123$

where $a_i = ith$ fibonacci number, $e$ is the Euler’s number and $x_i$ is a real variable (i.e. $a_1 = 1, a_2 = 1, a_3 = 2$ ..)

Let minimum value of: $e^{2 x_1} + e^{2 x_2} + … + e^{2 x_{30}}$ be $Z$ at $x_i = y_i$ where all $x_i$ satisfy the above condition.

Let $k = (y_1 + y_2 + y_3 + ... + y_{30})^4/Z$

Find the greatest integer $\le 100k$