\(3^{rd}\) round, November \(28^{th}\) 2015
A student called Slon is very mischievous in school. He is always bored in class and he is always
making a mess. The teacher wanted to calm him down and “tame” him, so he has given him a difficult
mathematical problem.
The teacher gives Slon an arithmetic expression \(A\), the integer \(P\) and \(M\). Slon has to answer the
following question: “What is the minimal n\(on-ne\)gative value of variable \(x\) in expression \(A\) so that
the remainder of dividing \(A\) with \(M\) is equal to \(P\)?”. The solution will always exist.
Additionally, it will hold that, if we apply the laws of distribution on expression \(A\), variable \(x\) will
not multiply variable \(x\) (formally, the expression is a polynomial of the first degree in variable \(x\)).
Examples of valid expressions \(A\): \(5 + x\) ∗(\(3 + 2\)), \(x + 3\) ∗\(x + 4\) ∗(\(5 + 3\) ∗(\(2 + x - 2\) ∗\(x\))).
Examples of invalid expressions \(A\): 5 ∗(\(3 + x\) ∗(\(3 + x\))), \(x\) ∗(\(x + x\) ∗(\(1 + x\))).

The first line of input contains the expression \(A\) (1 ⩽|\(A\)| ⩽100 000).
The second line of input contains two integers \(P\) (0 ⩽\(P\) ⩽\(M - 1\)) i \(M\) (1 ⩽\(M\) ⩽1 000 000).
The arithmetic expression A will only consists of characters +, -, *, (, ), x and digits from 0 to 9.
The brackets will always be paired, the operators +, - a\(nd * wi\)ll always be applied to exactly two
values (there will not be an expression (-5) or (4+-5)) and all multiplications will be explicit (there
will not be an expression 4(5) or 2(x)).

The first and only line of output must contain the minimal n\(on-ne\)gative value of variable \(x\).

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출처 COCI 2015/2016 Contest 3