k_{1} = \frac{4167}{25000}
k_{2} = \frac{1667}{100000}
k_{3} = \frac{19231}{100000}
k_{4} = \frac{1389}{25000}
k_{5} = 3
k_{6} = \frac{1}{1000}
k_{7} = 1
k_{8} = 330052960