Decomposition Reaction

A thermal decomposition reaction is breakdown of a compound into one or more compounds when heated. For example, $P \rightarrow a\cdot Q + b\cdot R$ is a decomposition reaction. Here, $1$ unit of $P$ is converted into $a$ unit of $Q$ and $b$ unit of $R$ after completion of the reaction. You are given $N$ compounds numbered from $1$ to $N$. The initial amount of the $i^{th}$ compound is $Q_i$.