Overloading the class subscript operator to access elements of a member std::vector object

I am parsing a text based file to read variables from it. Existence of variables in the file is important, so I decided to write a template class which will hold both value of the variable (Value) and its existence flag (Exists).

template<class Type>
class MyVariable
{
    public:
        Type    Value;
        bool    Exists;
        MyVariable()
            : Exists(false), Value(Type())
        {
        }
        MyVariable(const Type & Value)
            : Exists(true), Value(Value)
        {
        }
        MyVariable(const Type && Value)
            : Exists(true), Value(std::move(Value))
        {
        }
        MyVariable(const Type & Value, bool Existance)
            : Exists(Existance), Value(Value)
        {
        }
        MyVariable(const Type && Value, bool Existance)
            : Exists(Existance), Value(std::move(Value))
        {
        }
        size_t size() const
        {
            return Value.size();
        }
        const MyVariable & operator=(const MyVariable &  Another)
        {
            Value   = Another.Value;
            Exists  = true;
        }
        const MyVariable & operator=(const MyVariable && Another)
        {
            Value   = std::move(Another.Value);
            Exists  = true;
        }
        const Type & operator[](size_t Index) const
        {
            return Value[Index];
        }
              Type & operator[](size_t Index)
        {
            return Value[Index];
        }
        operator const Type & () const
        {
            Value;
        }
        operator Type &()
        {
            Value;
        }
};

The stored variable type will occasionally be std::vector, so I overloaded the subscript operator operator[] to directly access the elements of the vector. So that I can make the Value and Exists members private.

I use this class like this in the code:

const MyVariable<std::vector<int>> AVector({11, 22, 33, 44 ,55});
for (size_t i=0; i<AVector.size(); i++)
{
    std::wcout << L"Vector element #" << i << L" --> " << AVector.Value[i]  << std::endl;   // Works okay.
    std::wcout << L"Vector element #" << i << L" --> " << AVector[i]        << std::endl;   // Gives error.
}

I get the following error message:

Error C2679 binary '<<': no operator found which takes a right-hand operand of type 'const std::vector<int,std::allocator<_Ty>>' (or there is no acceptable conversion)

What am I doing wrong here?

TartanLlama's and songyuanyao's answers are correct only when the contained variable type (i.e.; ValueType) is std::vector. If we attempt to store a fundamental data type (e.g.; int or float), the compiler (MSVC14) gives the error below since there won't be any implicit subscript operator operator[] or value_type member type definition inside.

'InputFileVariable<bool,std::string>::value_type': is not a type name, static, or enumerator  
'InputFileVariable<int,std::string>::value_type': is not a type name, static, or enumerator  
'InputFileVariable<uintmax_t,std::string>::value_type': is not a type name, static, or enumerator  
'InputFileVariable<float,std::string>::value_type': is not a type name, static, or enumerator

I found the solution by using function templates. I rewrote the subscript operators as templates, so that the compiler doesn't create the subscript member functions unless they are called. And since I call them only when the stored element is an std::vector, it doesn't cause any problem with fundamental types.

My working final code is below.

#include <vector>
#include <string>

template<class ValueType, class KeyType = std::string>
class InputFileVariable
{
    public:
        const KeyType   Key;
        ValueType       Value;
        bool            Exists;
        InputFileVariable(KeyType && Key, ValueType && Value, bool Existance = false)
            :   Key     (std::forward<KeyType>  (Key)),
                Value   (std::forward<ValueType>(Value)),
                Exists  (Existance)
        {
        }
        size_t size() const
        {
            return Value.size();
        }
        const InputFileVariable & operator=(InputFileVariable && Another)
        {
            Key     = std::forward<InputFileVariable>(Another).Key;
            Value   = std::forward<InputFileVariable>(Another).Value;
            Exists  = true;
            return *this;
        }
        template <class ElementType = ValueType::value_type>
        const typename ElementType & operator[](size_t Index) const
        {
            return Value[Index];
        }
        template <class ElementType = ValueType::value_type>
        typename ElementType & operator[](size_t Index)
        {
            return Value[Index];
        }
        operator const ValueType & () const
        {
            return Value;
        }
        operator ValueType & ()
        {
            return Value;
        }
};

int wmain(int argc, wchar_t *argv[], wchar_t *envp[])
{
    // Used with "std::vector":
    InputFileVariable<std::vector<int>> MyVar1("MV1", {2, 4, 6, 8}, true);
    const size_t SIZE = MyVar1.size();
    std::cout << "Size = " << SIZE << std::endl;
    int Temp = MyVar1[1];
    MyVar1[1] = MyVar1[2];  // Here we call both the const and non-const operators.
    MyVar1[2] = Temp;
    for (size_t i=0; i<SIZE; i++)
    {
        std::cout << "MyVar1[" << i << "] = " << MyVar1[i] << std::endl;
    }

    // Used with "double":
    InputFileVariable<double> MyVar2("MV2", 3.14, true);
    std::cout << std::endl << "MyVar2    = " << MyVar2 << std::endl;

    std::cout << std::endl;
    _wsystem(L"timeout /t 60 /nobreak");
    return 0;
}

Output:

Size      = 4
MyVar1[0] = 2
MyVar1[1] = 6
MyVar1[2] = 4
MyVar1[3] = 8

MyVar2    = 3.14