I'd like to add information to a stack trace/exception.

Basically I've got something like this as of now, which I really like:

Exception in thread "main" java.lang.ArithmeticException: / by zero
    at com.so.main(SO.java:41)
    at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
    at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:39)
    at sun.reflect.DelegatingMethodAccessorImpl.invoke

However I'd like to catch that exception and add additional info to it, while still having the original stack trace.

For example, I'd like to have that:

Exception in thread "main" CustomException: / by zero (you tried to divide 42 by 0)
    at com.so.main(SO.java:41)
    at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
    at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:39)
    at sun.reflect.DelegatingMethodAccessorImpl.invoke

So basically I want to catch the ArithmeticException and rethrow, say, a CustomException (adding "you tried to divide 42 by 0" in this example) while still keeping the stacktrace from the original ArithmeticException.

What is the correct way to do this in Java?

Is the following correct:

try {
     ....
} catch (ArithmeticException e) {
     throw new CustomException( "You tried to divide " + x + " by " + y, e );
}