Food Portion Size

A university canteen never wants a student to leave hungry, so as long as a student is still hungry they may take another portion of food for free. To avoid wasting time, the canteen always serves one fixed portion size $S$ instead of first asking each student how much they want. Because of this, a student might not finish their final portion, and whatever is left over must be thrown away.

To keep costs down, the manager wants to choose a portion size $S$ so that little food is wasted while students also do not have to come back for more food too often. The two goals conflict:

• A very small $S$ wastes almost no food, but students must refill many times.
• A very large $S$ lets each student take just one portion, but a large amount of food may be wasted.

The manager has recorded how many units of food each student eats. Let $x$ be the total food wasted and let $y$ be the total number of times students go to fetch food. The goal is to minimize $a \cdot x + b \cdot y$, where the weights $a$ and $b$ express the relative importance of the two goals. Both $x$ and $y$ depend on the portion size $S$ (which may be any positive real value) and on how much each student eats. One extra rule applies: no student may fetch food more than $3$ times.

The input contains several test cases. Each test case begins with a line containing an integer $n$ ($1 \le n \le 1000$), the number of students. The next line contains two integers $a$ and $b$ ($1 \le a, b \le 10$). The third line contains $n$ integers $y_1, \ldots, y_n$ ($1 \le y_i \le 100$), where $y_i$ is the number of food units that student $i$ eats. The input ends with a line containing $n = 0$, which should not be processed.

For each test case, print one line with the minimum possible value of $a \cdot x + b \cdot y$ over all valid portion sizes. Print the value as a reduced fraction in the form p / q. If the value is an integer, print only the numerator and omit the denominator $1$.