Revise paste Untitled

#include <iostream>

using namespace std;
string add_big_integer(string A, string B) { // funkcija koja ke ni sobere A + B
    if(A.size() < B.size()) {
        swap(A, B);
    }
    int a_i = (int) A.size() - 1;
    int b_i = (int) B.size() - 1;
    int carry = 0;
    string sum = "";
    while(a_i >= 0 and b_i >= 0) {
        int digit_a = (A[a_i] - '0');
        int digit_b = (B[b_i] - '0');
        int zbir = digit_a + digit_b + carry;
        
        if(zbir <= 9) {
            sum += (zbir + '0');
            carry = 0;
        }
        else {
            carry = 1;
            zbir -= 10;
            sum += (zbir + '0');
        }
        a_i--;
        b_i--;
    }
    while(a_i >= 0) {
        int digit_a = (A[a_i] - '0');
        int zbir = digit_a + carry;
        if(zbir <= 9) {
            sum += (zbir + '0');
            carry = 0;
        }
        else {
            carry = 1;
            zbir -= 10;
            sum += (zbir + '0');
        }
        a_i--;
    }
    if(carry == 1) {
        sum += "1";
    }
    reverse(sum.begin(), sum.end());
    return sum;
}
int main()
{
    string a, b;
    cin >> a >> b;
    cout << add_big_integer(a, b) << endl;
    return 0;
}