string addStrings(string num1, string num2) {

string& longstr = ( num1.size() >= num2.size() ? num1 : num2 );

string& shortstr = ( num1.size() < num2.size() ? num1 : num2 );

int longlen = longstr.size();

int shortlen = shortstr.size();

char carry = 0;

int i, j;

string result;

for (i = longlen-1, j=shortlen-1; i>=0; i--, j--) {

int add = 0;

if (j>=0) {

add = longstr[i] + shortstr[j] - 2 * '0' + carry;

}else{

add = longstr[i] - '0' + carry;

}

carry = add/10;

result = char('0' + add % 10) + result;

}

if (carry) {

result = '1' + result;

}

return result;

}