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 $10^9 + 7$.

有一个长度为 $l$ 的泳池，$n$ 名游泳者计划在此游泳。所有人同时开始游泳（即在时刻 $0$ 开始），但你可以假设他们使用不同的泳道，因此彼此之间不会相互干扰。

每个人的游泳路线如下：从位置 $0$ 出发，以恒定速度（第 $i$ 名游泳者的速度为 $v_i$ 单位/秒）游向位置 $l$；到达位置 $l$ 后，立即（耗时可忽略不计）转身，并以相同的速度返回游向位置 $0$；回到位置 $0$ 后，再次转向游向位置 $l$，如此往复。

我们称某个实数时刻为相遇时刻，当且仅当在该时刻，至少有两名游泳者恰好位于泳池中的同一位置（该位置可以是端点 $0$ 或 $l$，也可以是泳池内部任意实数位置）。

泳池开放时长为 $t$ 秒。你需要计算在泳池开放期间发生的相遇时刻的总数。由于答案可能非常大，请对 $10^9 + 7$ 取模后输出。

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.

第一行包含两个整数 $l$ 和 $t$（$1 \le l, t \le 10^9$）—— 分别表示泳池的长度和过程持续时间（单位：秒）。

第二行包含一个整数 $n$（$2 \le n \le 2 \cdot 10^5$）—— 表示游泳者的数量。

第三行包含 $n$ 个整数 $v_1, v_2, \dots, v_n$（$1 \le v_i \le 2 \cdot 10^5$），其中 $v_i$ 表示第 $i$ 个游泳者的速度。所有 $v_i$ 两两互不相同。

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

输出一个整数——相遇时刻的数量（包括时刻 $t$（若需要），但不包括时刻 $0$），对 $10^9 + 7$ 取模。

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 $0$.

在第一个示例中，存在三次相遇时刻：

• 时刻 $6$，此时两名游泳者均位于位置 $6$；
• 时刻 $12$，此时两名游泳者均位于位置 $6$；
• 以及时刻 $18$，此时两名游泳者均位于位置 $0$。