Context submenu with arrow navigation doesnt navigate to child item

#include <QtGui>
#include <QApplication>
#include <QMenu>
#include <QContextMenuEvent>

class Foo : public QWidget
{
public:
    Foo() : QWidget(0) {resize(200,200);}

    void contextMenuEvent(QContextMenuEvent* event)
    {
        QMenu menu("Menu");
        QMenu* subMenu = new QMenu("Parent", &menu);
        menu.addMenu(subMenu);
        subMenu->addAction("Child Item");

        menu.exec(event->globalPos());
    }

};

int main(int argc, char* argv[])
{
    QApplication app(argc, argv);
    Foo foo;
    foo.show();
    return app.exec();
}