John and his Game

John wants to play a game with you. He has an integer with him, S, but he has hid it from you. Instead, he has shared some information about S. In particular, for every i such that 1 ≤ i ≤ N, he has told you the value ⌊(i*S)/K⌋. This is given to you as the array A1, A2, ..., AN, where Ai = ⌊(i*S)/K⌋. He has also told you the value of K. But since he has not shared the value of S, you want to find