How to write proper std::initializer_list constructor

Consider following code:

#include <iostream>
#include <vector>

struct C {
    std::vector<int> a;
    std::string b;
    bool c;
};

void printC(const C &c) {
    // ...
}

int main() {
    printC({
        { 1, 2, 3 },
        "ehlo",
        false
    });
}

This works, because compiler can generate proper constructor for me. But if I change struct C to this:

struct C {
    std::vector<int> a;
    std::string b;
    bool c;

    C() {
        c = false;
    }
};

The printC call stops working because compiler stops generating appropriate constructor. I've tried to write myself a constructor using std::initializer_list but failed.

So the question is - How to write constructor that will make the above code compile and work again?