Football

Every year, student sports competitions are held in Byteland. Football is especially popular and is played by $N$ students; the skill of student $i$ as a footballer is given by the integer $A_i$.

For the tournament, $K$ teams must be formed, and every team must have at least $M$ players. The strength of a team is the arithmetic mean of the skills of its members. For example, if a team has players with skills $1$, $5$, $4$ and $9$, then the strength of that team is $\frac{1+5+4+9}{4} = 4.75$.

The coach wrote all players' skills on paper in a single row. He now wants to split this row into $K$ segments so that each segment contains at least $M$ numbers. He then forms one team from the players in each segment. To make the tournament more exciting, the coach wants the strength of the weakest team to be as large as possible.

For example, if the players' skills in order are $5$, $4$, $4$, $3$, $5$, $1$ and $8$, and two teams must be formed with at least three players each, the coach has two options:

• put the players with skills $5$, $4$, $4$ in the first team and $3$, $5$, $1$, $8$ in the second team;
• put the players with skills $5$, $4$, $4$, $3$ in the first team and $5$, $1$, $8$ in the second team.

In the first case the strength of the weaker team is $\frac{17}{4}=4.25$; in the second case it is $4$. So the coach chooses the first option.

Write a program that, for the given players, determines the largest possible strength of the weakest team.

The first line contains three space-separated integers $N$, $M$ and $K$ ($6 \le N \le 10^4$, $2 \le M$, $2 \le K \le 500$, $K \cdot M \le N$): the number of players, the minimum required team size, and the number of teams to form, respectively.

The second line contains $N$ space-separated integers $A_i$ ($1 \le A_i \le 10^9$): the players' skills, in order.

Divide the players, in the given order, into $K$ consecutive teams of at least $M$ players each. Print, on a single line, the largest possible strength of the weakest team as a reduced fraction $p/q$ (in lowest terms, with denominator $q \ge 1$). If the value is an integer $v$, print it as $v/1$.