C++: how to override std::bad_alloc exception on my own class?

I'm trying to override std::bad_alloc in my own exception class like in the code given below

#include <iostream>
#include <exception>

class my_exception: public std::bad_alloc {
    public:
        my_exception() {};
        virtual const char* what() const throw() {
            return "Memory Error: Can't allocate enough memory";
        }
};

class can_throw_exception {
    public:
        can_throw_exception() {};
        void throw_exception() {
            int* p = new int[9999999999999999999999];
            delete [] p;
        }
};


int main() {
    try {
        can_throw_exception c;
        c.throw_exception();
    }
    catch(const my_exception& error) {
        std::cout << error.what() << std::endl;
    }
    return 0;
}

But when I run this code, I get this message

terminate called after throwing an instance of 'std::bad_alloc'
what(): std::bad_alloc Aborted (core dumped)

Which means that my version of what() function didn't been called. How to override correctly std::bad_alloc exception ?