Is it possible to combine default member initialization and delegating constructors?

Question

Suppose I have a class

class Widget
{
public:
    explicit Widget();
    explicit Widget(int foo, int bar);

private:
    Gadget * gadget_;
    int foo_{42};
    int bar_{13};
}

with constructors that use some members (therefore initialization order is important):

Widget::Widget()
{
    ComplicatedConstructionStandIn::frobnicate_gadget(&gadget_);
    TheConstructorHasManyLines(foo_, gadget_);
    ItDoesMultipleThings(bar_);
}

Widget::Widget(int foo, int bar)
    : foo_{foo}
    , bar_{bar}
{
    ComplicatedConstructionStandIn::frobnicate_gadget(&gadget_);
    TheConstructorHasManyLines(foo_, gadget_);
    ItDoesMultipleThings(bar_);
}

Clearly, the second constructor is code duplication so you would think to delegate !BUT! you can't do that if you also want the default member initialization (int foo{42};). By delegation I mean something like this (does not compile):

Widget::Widget(int foo, int bar)
    : foo_{foo}
    , bar_{bar}
    , Widget()
{}

Is there an elegant way out of this? Wrapping the body of the constructor in an auxiliary init function is just kicking the question down the line.