CF1845F Swimmers in the Pool

There is a pool of length $ l $ where $ n $ swimmers plan to swim. People start swimming at the same time (at the time moment $ 0 $ ), but you can assume that they take different lanes, so they don't interfere with each other. Each person swims along the following route: they start at point $ 0 $ and swim to point $ l $ with constant speed (which is equal to $ v_i $ units per second for the $ i $ -th swimmer). After reaching the point $ l $ , the swimmer instantly (in negligible time) turns back and starts swimming to the point $ 0 $ with the same constant speed. After returning to the point $ 0 $ , the swimmer starts swimming to the point $ l $ , and so on. Let's say that some real moment of time is a meeting moment if there are at least two swimmers that are in the same point of the pool at that moment of time (that point may be $ 0 $ or $ l $ as well as any other real point inside the pool). The pool will be open for $ t $ seconds. You have to calculate the number of meeting moments while the pool is open. Since the answer may be very large, print it modulo $ 10^9 + 7 $ .

The first line contains two integers $ l $ and $ t $ ( $ 1 \le l, t \le 10^9 $ ) — the length of the pool and the duration of the process (in seconds). The second line contains the single integer $ n $ ( $ 2 \le n \le 2 \cdot 10^5 $ ) — the number of swimmers. The third line contains $ n $ integers $ v_1, v_2, \dots, v_n $ ( $ 1 \le v_i \le 2 \cdot 10^5 $ ), where $ v_i $ is the speed of the $ i $ -th swimmer. All $ v_i $ are pairwise distinct.

Print one integer — the number of meeting moments (including moment $ t $ if needed and excluding moment $ 0 $ ), taken modulo $ 10^9 + 7 $ .

In the first example, there are three meeting moments: - moment $ 6 $ , during which both swimmers are in the point $ 6 $ ; - moment $ 12 $ , during which both swimmers are in the point $ 6 $ ; - and moment $ 18 $ , during which both swimmers are in the point $ 0 $ .