请设计一个算法能够完成两个用字符串存储的整数进行相加操作，对非法的输入则返回error

#include <iostream>
#include <string>
#include<algorithm>
using namespace std;
int main(){
    string str1;
    string str2;
    while(cin>>str1>>str2){
        int size1 = str1.size()-1;
        int size2 = str2.size()-1;
        int flag = 0;
        for(int i=0;i<=size1;i++){
            if(!(str1[i]>='0' && str1[i] <= '9')){
                cout<<"error"<<endl;
                flag = 1;
                break;
            }
        }
        if(flag) break;
        for(int i=0;i<=size2;i++){
             if(!(str2[i]>='0' && str2[i] <= '9')){
                cout<<"error"<<endl;
                 flag = 1;
                break;
            }
        }
        if(flag) break;
        string sum;
        int carry = 0;
        int j = 0;
        while(size1>=0 && size2>=0){
            int nsum = (str1[size1] - '0') + (str2[size2] - '0') + carry;
            carry = nsum/10;
            nsum = nsum%10;
            sum += to_string(nsum);
            size1--;
            size2--;
        }
        while(size1 >= 0){
            int nsum = (str1[size1] - '0') + carry;
            carry = nsum/10;
            nsum = nsum%10;
            sum += to_string(nsum);
            size1--;
        }
        while(size2 >= 0){
            int nsum = (str2[size2] - '0') + carry;
            carry = nsum/10;
            nsum = nsum%10;
            sum += to_string(nsum);
            size2--;
        }
        if(carry){
            sum += '1';
        }
        reverse(sum.begin(),sum.end());
        cout<<sum<<endl;
    }
}