The condition from the task is that the expression is a first degree polynomial of the form $ax+b$. Let $f(x)=ax+b$. If we calculate the expression at $0$, we will see that $f(0)=b$. If we calculate it at $1$, we will see that $f(1)=a+b$. This gives us values $a$ and $b$. We are left to figure out how to calculate the minimal value of $x$ such that $ax+b\equiv p(\mathrm{mod}m)$. Given that $m\le {10}^6$, we can iterate over all values of $x$ until we find the minimal value that satisfies the upper equation. We are left to figure out how to calculate the expression at $0$ and $1$.

One of the ways we can do this is using the command eval in Python. Another way is to parse the expression from infix to postfix notation using the "shunting-yard" algorithm. Another approach is to convert the expression to postfix notation and then the addition, multiplication and subtraction is performed over polynomials with maximal degree of $1$ and, finally, the same equation of the form $ax+b\equiv p(\mathrm{mod}m)$ is solved.