CF28C.Bath Queue

There are n students living in the campus. Every morning all students wake up at the same time and go to wash. There are m rooms with wash basins. The i-th of these rooms contains a__i wash basins. Every student independently select one the rooms with equal probability and goes to it. After all students selected their rooms, students in each room divide into queues by the number of wash basins so that the size of the largest queue is the least possible. Calculate the expected value of the size of the largest queue among all rooms.

校园里有 $n$ 名学生。每天早晨，所有学生同时醒来并去洗漱。 campus 里有 $m$ 个配备洗手池的房间，其中第 $i$ 个房间有 $a_i$ 个洗手池。每名学生独立地、以相等的概率随机选择一个房间前往。在所有学生都选定房间后，每个房间内的学生会根据该房间的洗手池数量排成若干队列，使得该房间内最长队列的长度尽可能小。请计算所有房间中最长队列长度的期望值。

The first line contains two positive integers n and m (1 ≤ n, m ≤ 50) — the amount of students and the amount of rooms. The second line contains m integers _a_1, _a_2, ... , a__m (1 ≤ a__i ≤ 50). a__i means the amount of wash basins in the i-th room.

第一行包含两个正整数 $n$ 和 $m$（$1 \leq n, m \leq 50$）—— 分别表示学生的数量和房间的数量。
第二行包含 $m$ 个整数 $a_1, a_2, \ldots, a_m$（$1 \leq a_i \leq 50$）。其中 $a_i$ 表示第 $i$ 个房间中的洗手池数量。

Output single number: the expected value of the size of the largest queue. Your answer must have an absolute or relative error less than 10 - 9.

输出一个数字：最大队列长度的期望值。你的答案的绝对或相对误差必须小于 $10^{-9}$。