+107 Rationalize the denominator of \(\frac{\sqrt{32}}{\sqrt{16}-\sqrt{2}} \). The answer can be written as \(\frac{A\sqrt{B}+C}{D}\), where A, B, C, and D are integers, D is positive, and B is not divisible by the square of any prime. Find the minimum possible value of \(A+B+C+D\).
