Intense heat

The temperature over $n$ days is known: on day $i$ it is $a_i$ degrees. The average temperature of a block of consecutive days of length at least $k$ is the sum of its temperatures divided by the number of days. Find the maximum average temperature over all such blocks.

The first line contains $n$ and $k$ ($1 \le k \le n \le 2000$). The second line contains $n$ integers ($1 \le a_i \le 5000$).

Print the answer as an irreducible fraction p/q, where $p$ and $q$ are coprime positive integers. The denominator is printed even for an integer answer, for example 5/1.

With prefix sums the sum of any block takes $O(1)$, so checking all blocks is $O(n^2)$ — $2 \cdot 10^6$ operations for $n = 2000$. Compare fractions without floating point: $\frac{s_1}{l_1} < \frac{s_2}{l_2} \iff s_1 l_2 < s_2 l_1$. Finally divide $p$ and $q$ by their GCD.

In the example the best block is $3, 4, 1$ with average $8/3$.

Source: Codeforces, problem 1003C.