function as a string??

[afleury1]

I am working on a program that needs to request user to enter positive 2 numbers.
The following is what my code is currently:

  #include <iostream>
  #include <string>
  #include <cstdlib>

using namespace std;

void count_up (int a, int b=0);
void count_down (int a, int b=0);
void count_between (int a, int b);
void get_positiveNumbers(int& a, int& b);

int main()
{
   int firstNum;
   int secondNum;
   char answer;

 do
 {
  get_positiveNumbers(firstNum, secondNum);
  count_up(firstNum);
  count_down(firstNum);
  count_between(firstNum, secondNum);

  cout << "Would you like to try again?" <<endl;
  cin>> answer;
 }while (answer == 'y');
 return0;
}
 void get_positiveNumbers (int& a, int& b)
 {
  cout<< "Enter 2 numbers, please;" <<endl;
  cin >>a;
  cin >>b;
 while (a<=0 ||b<=0 && ((int)a !=a ||(int)b != b))
   {
    cout<< "You did not enter 2 positive numbers, please try again:" << endl;
    cin >>a;
    cin >>b;
   }
  }
 void count_up(int a, int b)
 {
  do
  {
  cout<< b << " ";
  }while (b++ !=a);
   cout>> endl;
 }
 void count_down(int a, int b)
 {
  do
  {
   cout<< a << " ";
  }while (a-- !=b);
  cout << endl;
 }
void count_between (int a, int b)
{
 if (a < b)
 {
  count_up(b, a)
 }
 else
 {
  count_down(a,b)
 }
}

So, as it is everything is working as expected, except. when the user enters a positive number for the first number and a negative number for the second number. The program should respond "you did not enter 2 positive numbers". It runs the program as if two positive numbers were entered....
I know the problem is in the while loop somehow....

Also, I am supposed to somehow change the get_positiveNumbers function so that call for a function that gets the input as a string
interpret if the string is positive
then convert it to an integer and sends it back to the main function

I am totally lost on how to do this...

Any help is appreciated. Thank you!