C++ default brace-enclosed initializer list

Let's say I have c_student class with several members and no constructors:

#include <iostream>
#include <string>
#include <initializer_list>
#include <typeinfo>

class c_student{
    // private:
    public:
        std::string name = "John";
        int         mark = 5;
        std::string second_name="Doe";

        void print(){
            std::cout << name <<" " << second_name << " : "<< mark<<"\n";
        }
    };

int main(){
    c_student stud_c  = {"Luke ",420};
    stud_c.print();
    c_student stud_d  = {"Mark "};
    stud_d.print();
        
}

This code works fine, but let's say I want to define custom constructors inside the class:

        c_student (std::string n):name(n){};
        c_student() = default;

If I add them to class, the compiler complains that:

47_object_initialization.cpp:32:34: error: could not convert ‘{"Luke ", 420}’ from ‘<brace-enclosed initializer list>’ to ‘c_student’
   32 |  c_student stud_c  = {"Luke ",420};
      |                                  ^
      |                                  |
      |                                  <brace-enclosed initializer list>

I want to keep using default constructor for {} and so need to write something like:

c_student( std::initializer_list <???>) = default; << Pseudo-code only!

But can't get how exactly. Could anyone points my attention on the right page of CPP reference?