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 \pmod{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 \pmod{m}~ is solved.