Shmerlin the magician found the door to the Cave of Wisdom. The door is guarded by Drago the Math Dragon, and also locked with a 4-digit lock. Drago agrees to put Shmerlin to the test: Shmerlin has to choose four integer numbers: \(x, y, z\) and \(w\), and the dragon will tell him the value of \(A \times x + B \times y + C \times z + D \times w\), where \(A, B, C\) and \(D\) are the four secret digits that open the lock. After that, Shmerlin should come up with a guess of the secret digits. If the guess is correct, Drago will let the magician into the cave. Otherwise, Shmerlin will perish. Does Shmerlin have a way to succeed?