Cartesian product of streams in Java 8 as stream (using streams only)

Question

I would like to create a method which creates a stream of elements which are cartesian products of multiple given streams (aggregated to the same type at the end by a binary operator). Please note that both arguments and results are streams, not collections.

For example, for two streams of {A, B} and {X, Y} I would like it produce stream of values {AX, AY, BX, BY} (simple concatenation is used for aggregating the strings). So far, I have came up with this code:

private static <T> Stream<T> cartesian(BinaryOperator<T> aggregator, Stream<T>... streams) {
    Stream<T> result = null;

    for (Stream<T> stream : streams) {
        if (result == null) {
            result = stream;
        } else {
            result = result.flatMap(m -> stream.map(n -> aggregator.apply(m, n)));
        }
    }

    return result;
}

This is my desired use case:

Stream<String> result = cartesian(
  (a, b) -> a + b, 
  Stream.of("A", "B"), 
  Stream.of("X", "Y")
);

System.out.println(result.collect(Collectors.toList()));

Expected result: AX, AY, BX, BY.

Another example:

Stream<String> result = cartesian(
  (a, b) -> a + b, 
  Stream.of("A", "B"), 
  Stream.of("K", "L"), 
  Stream.of("X", "Y")
);

Expected result: AKX, AKY, ALX, ALY, BKX, BKY, BLX, BLY.

However, if I run the code, I get this error:

IllegalStateException: stream has already been operated upon or closed

Where is the stream consumed? By flatMap? Can it be easily fixed?