It's All In The Mind

Professor Zhang has a number sequence $a\_1, a\_2, \ldots, a\_n$. However, the sequence is not complete and some elements are missing. Fortunately, Professor Zhang remembers some attributes of the sequence:

• For every $i \in \\{1, 2, \ldots, n\\}$, $0 \le a\_i \le 100$.
• The sequence is non-increasing: $a\_1 \ge a\_2 \ge \ldots \ge a\_n$.
• The sum of all elements in the sequence is not zero.

Professor Zhang wants to know the maximum value of $\frac{a\_1 + a\_2}{\sum\_{i = 1}^{n}{a\_i}}$ among all the possible sequences.

There are multiple test cases. The first line of input contains an integer $T$ indicating the number of test cases. For each test case:

The first line contains two integers $n$ and $m$ ($2 \le n \le 100$, $0 \le m \le n$): the length of the sequence and the number of known elements.

Each of the next $m$ lines contains two integers $x\_i$ and $y\_i$ ($1 \le x\_i \le n$, $0 \le y\_i \le 100$, $x\_i < x\_{i + 1}$, $y\_i \ge y\_{i + 1}$) indicating that $a\_{x\_i} = y\_i$.

There are at most $2000$ test cases, and the total size of the input is no more than $350$ kibibytes.

For each test case, output the answer as an irreducible fraction $p$/$q$ where $p$ and $q$ are integers, and $q > 0$.