Gargle

Google once put up the following billboard along Highway 101, which runs through the heart of Silicon Valley:

"{first 10-digit prime found in consecutive digits of $e$}.com"

Deeply impressed by this recruiting stunt, a mouthwash company named Gargle decided to hire people with the following problem:

"{the digits of a certain rational number written in base 7, from the $B$-th digit through the $E$-th digit after the radix point}.com"

For example, $\frac{1}{5}$ (in base 10) written in base 7 is $0.12541\ldots_{(7)}$, $\frac{33}{4}$ is $11.15151\ldots_{(7)}$, and $\frac{6}{49}$ is $0.06000\ldots_{(7)}$.

Given a rational number $\frac{N}{D}$, write a program that prints its base-7 digits from the $B$-th digit through the $E$-th digit after the radix point.

The first line contains the number of test cases $T$.

Each test case is given on a single line as four base-10 integers $N$, $D$, $B$, and $E$ separated by spaces. $N$ and $D$ are the numerator and denominator of the rational number, with $0 \le N \le 5{,}000$ and $1 \le D \le 5{,}000$. $B$ and $E$ give the range of digit positions to output, with $0 \le B, E \le 250$ and $0 \le E - B \le 20$.

The $0$-th digit after the radix point is the digit immediately to the right of the point.

For each test case, print one line in the following format:

Problem set k: N / D, base 7 digits B through E: result

Here $k$ is the test case number (starting from 1), $result$ is the computed digit string, and the other values $N$, $D$, $B$, $E$ are those given in the input. Leading zeros in $result$ are printed as-is.