string multiply(string num1, string num2) {

int m = num1.size();

int n = num2.size();

string result(m + n, '0');

for (int i = m - 1; i >= 0; i--) {

for (int j = n - 1; j >= 0; j--) {

int sum = (num1[i] - '0') * (num2[j] - '0') + (result[i + j + 1] - '0');

result[i + j + 1] = sum % 10 + '0';

result[i + j] += sum / 10;

}

}

for (int i = 0; i < m + n; i++) {

if (result[i] != '0') {

return result.substr(i);

}

}

return "0";

}