After you determine what the program of Exercise 5.45 does, modify the program to func- tion properly after removing the restriction that the second argument be nonnegative.

What will be an ideal response?

```
// Multiply integers (positive or negative) using recursion.
#include
using namespace std;

int mystery( int, int ); // function prototype

int main()
{
int x; // first integer
int y; // second integer

cout << "Enter two integers: ";
cin >> x >> y;
cout << "The result is " << mystery( x, y ) << endl;
} // end main

// mystery multiplies a * b using recursion
int mystery( int a, int b )
{
if ( b < 0 ) // if b is negative
{
// multiply both a and b by -1, so b is positive
// note this multiplies answer by (-1)*(-1) = 1
a *= -1;
b *= -1;
} // end if

if ( b == 1 ) // base case
return a;
else // recursion step
return a + mystery( a, b - 1 );
} // end function mystery
```