We've Got Chemistry, Babe

Barry is a chemistry student who does well except at one thing: balancing chemical equations. A chemical reaction is written as a chemical equation, with the reactants on the left and the products on the right, separated by an arrow. For example, forming aluminum oxide from aluminum and oxygen is written Al + O2 -> Al2O3.

This equation is not balanced: there is one aluminum (Al) atom on the left and two on the right, and there are two oxygen (O) atoms on the left and three on the right. A properly balanced version is 4Al + 3O2 -> 2Al2O3.

When an equation is balanced, all of its coefficients must be positive integers whose greatest common divisor is $1$. Harder equations also arise, such as Fe2(SO4)3 + KSCN -> K3Fe(SCN)6 + K2SO4.

The atoms inside a pair of parentheses are all multiplied by the number that immediately follows the closing parenthesis (so this equation has 12 oxygen atoms on the left and six carbon (C) atoms on the right). A chemical symbol appears at most once within any single reactant or product. Given a reaction, determine the coefficients that balance it.

The input contains several test cases. Each test case is a single line that begins with two positive integers $r$ and $p$, the number of reactants and the number of products (each at most $10$). Then come the $r$ reactants and, after them, the $p$ products, all separated by spaces. Each reactant or product is a formula built from one or more terms, where a term is a single chemical symbol, a chemical symbol followed by an integer $\ge 2$, or a parenthesized formula (one or more terms) followed by an integer $\ge 2$. Every chemical symbol is one or two letters, only the first of which is capitalized. No test case uses more than $20$ distinct chemical symbols. A line containing two zeros terminates the input and is not processed.

For each test case, output Case X: (where X is the test case number, starting from $1$) followed by the coefficients that balance the equation, in the order the reactants and then the products were given, separated by single spaces. If the equation cannot be balanced at all, or if it can be balanced but not uniquely (more than one set of coefficients works, ignoring common multiples), output the word No instead of the coefficients.