Figure Out the Base

What is $6$ times $9$? The answer is $42$. If you thought it was $54$, take a short break before continuing — because $42$ is the result when the arithmetic is done in base $13$.

For an integer $B \ge 2$, every digit of a base-$B$ number is an integer between $0$ and $B-1$. To read a base-$B$ number, multiply the rightmost digit by $1$, the next digit to the left by $B$, the next by $B^2$, and so on, then add everything up.

Whether an equation is true can depend on the base being used. For example, $2+2=4$ is always true when $B \ge 5$: base $4$ cannot use the digit $4$, so $B$ must be at least $5$. On the other hand, an equation such as $2+2=5$ can never be true in any base.

Given an equation, write a program that determines in which bases the equation is true.

Each line of input is one test case of the form EXPR=EXPR. EXPR is an expression whose length does not exceed $17$.

Every expression is always valid and consists only of +, *, and the digits 0 through 9. No expression starts with +, and no number has unnecessary leading zeros.

The last line of input contains a single =.

For each test case, print the bases in which the given equation is true.

If infinitely many bases make the equation true, print B+, where $B$ is the smallest such base.

If the number of such bases is finite, print them in ascending order separated by spaces.

If no base makes the equation true, print *.