Magnetism makes things Interesting - 1

A particle with mass \(m\) and charge \(q\) is thrown up with initial speed \(\vec{v_{0}}=(0,0,v_{0})\) in the presence of a magnetic field \(\vec{B}=(B_{0},0,0)\) and a gravitational field \(\vec{g}=(0,0,-g)\). If we are known that \(v_{0}=\frac{mg}{qB_{0}}\), the first time for which the particle gets its maximmum height can be written as \(T=\frac{a\cdot \pi \cdot v_{0}}{b\cdot g}\) find the value of \(a+b\)

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