matrices – Find the matrix P with all $P_{ij} geq 0$ that satisfies the equation $PX=Y$?

For a project, I have to find the matrix $P$ with all non-negative entries $P_{ij} geq 0$ that satisfies the equation $PX=Y$. All of the entries $P_{ij}$ of the matrix $P$ must be non-negative real numbers. The entries of $X$ and $Y$ are all non-negative real numbers. Matrix $P$ is $m$ by $n$, matrix $X$ is $n$ by $r$, and matrix $Y$ is $n$ by $q$.
I tried the solution: $P$=$Y$($X$$X’$)^$-1$ but this solution does not always satisfy the $P_{ij} geq 0$ condition. There should be a solution that always satisfies the condition.