RealPhobia

Bert is a programmer who is genuinely afraid of floating-point arithmetic. He has had great success writing his programs with rational numbers instead, but he dislikes it when a denominator grows large.

Help Bert by writing a program that lowers the denominator of a rational number while introducing the smallest possible error. For a rational number $A/B$ with $B > 2$ and $0 < A < B$, find a rational number $C/D$ such that:

1. $0 < C < D < B$;
2. the error $\left|\dfrac{A}{B} - \dfrac{C}{D}\right|$ is the minimum over all valid $C$ and $D$; and
3. among all pairs achieving that minimum error, $D$ is the smallest possible positive integer.

Because condition 3 minimises $D$, the answer fraction $C/D$ is always already in lowest terms.

The first line contains an integer $K$ ($1 < K < 1000$), the number of test cases. Each of the next $K$ lines contains one test case: a fraction written as two integers $A$ and $B$ separated by a slash (/), where

1. $B$ is a 32-bit integer strictly greater than $2$, and
2. $0 < A < B$.

For each test case, print one line containing the fraction $C/D$, written as two integers separated by a slash (/).