We introduce an exact solution for atom-molecule conversion in a heteronuclear triatomic system in terms of inverse engineering. Since the processes of molecular synthesis and decomposition occur simultaneously, the kinetics become more complicated, but our solution captures the detailed evolution of main and side reactions. Additionally, we further analyze the minimal time $T_{min}$ and energy consumption for the system from an initial state to a given target state, and also investigate the dynamics when two conversion pathways coexist, in which the dynamics will deviate from those of the original single-path scheme.

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• Exotic atoms & molecules
• Population dynamics
• Reaction diffusion systems
• Rydberg atoms & molecules
• Trapped atoms
• Trapped ions
• Ultracold gases
• Cooling & trapping
• Information theory
• Two-level models