# Problem M

Methodic Multiplication

The Peano axioms (named after Italian mathematican Giuseppe
Peano) are an axiomatic formalization of the arithmetic
properties of the natural numbers. We have two symbols: the
constant $0$, and a unary
successor function $S$.
The natural numbers, starting at $0$, are then $0$, $S(0)$, $S(S(0))$, $S(S(S(0)))$, and so on. With these
two symbols, the operations of *addition* and
*multiplication* are defined inductively by the
following axioms: for any natural numbers $x$ and $y$, we have

The two axioms on the left define addition, and the two on the right define multiplication.

For instance, given $x = S(S(0))$ and $y = S(0)$ we can repeatedly apply these axioms to derive

\begin{align*} x \cdot y & = S(S(0)) \cdot S(0) = S(S(0)) \cdot 0 + S(S(0))\\ & = 0 + S(S(0)) = S(0 + S(0)) = S(S(0 + 0)) = S(S(0)) \end{align*}Write a program which given two natural numbers $x$ and $y$, defined in Peano arithmetic, computes the product $x \cdot y$.

## Input

The input consists of two lines. Each line contains a natural number defined in Peano arithmatic, using at most $1\, 000$ characters.

## Output

Output the product of the two input numbers.

Sample Input 1 | Sample Output 1 |
---|---|

S(S(0)) S(S(S(0))) |
S(S(S(S(S(S(0)))))) |

Sample Input 2 | Sample Output 2 |
---|---|

S(S(S(S(S(0))))) 0 |
0 |