What is the size limit for a C++ number?

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C++

So I have a 340 digit number(actually many numbers of similar length):

1129711511511911111410096234183176109119206163129208102132631072477671382311641228010717710121397160216130941034422491351531952542142042212010417692502361865016015813621817721819614024011173210721117018713290631941066622184168211118201220201551611586422931177241021224113946112515922518478624313439126015210223973231982481351582251272696193

I need some way to convert it to an int(it's a string right now). I am able to have a variable that big in Python, but now I'm working in c++.

What I have tried:

I need it as an int so I can run it through a function I have:

string decimalToBinary(vector<int> decimal, int length = 7)
{
    string binary;

    for (int dec: decimal)
    {
        for (int i = length; i >= 0; i--) 
        { 
            int k = dec >> i; 
            if (k & 1) 
            {
                binary.append("1");
            } 
            else
            {
                binary.append("0");
            }
        } 
    }
    return binary;
}

I've tried converting it with std::stoll, but I still get the 'out_or_range' error. Is there any way to do this, or do it without converting to int?