string addBinary(string a, string b) {

int len = max(a.size(),b.size());

vector<string> result(len,"0");

int i=a.size()-1,j=b.size()-1,k=len-1;

int advance=0,isum=0;

while(i>=0||j>=0){

if(i<0) isum=(b[j]-'0')+advance;

else if(j<0) isum=(a[i]-'0')+advance;

else isum=(a[i]-'0')+(b[j]-'0')+advance;

advance=0;

advance = isum/2;

result[k]=to_string(isum%2);

i--;

j--;

k--;

}

string res="";

if(advance>0) {

res += "1";

}

for(int i=0;i<len;++i){

res += result[i];

}

return res;

}