2710：Consecutive Digits

As a recruiting ploy, Google once posted billboards in Harvard Square and in the Silicon Valley area just stating “{first 10-digit prime found in consecutive digits of e}.com”. In other words, find that 10-digit sequence and then connect to the web site — and find out that Google is trying to hire people who can solve a particular kind of problem.

Not to be outdone, Gaggle (a loosy-goosy fuzzy logic search firm), has devised its own recruiting problem. Consider the base 7 expansion of a rational number. For example, the first few digits of the base 7 expansion of 1/5₁₀ = 0.12541...₇, 33/4₁₀ = 11.15151...₇, and 6/49₁₀ = 0.06000...₇, From this expansion, find the digits in a particular range of positions to the right of the "decimal" point.

The input file begins with a line containing a single integer specifying the number of problem sets in the file. Each problem set is specified by four base 10 numbers on a single line, n d b e, where n and d are the numerator and denominator of the rational number and 0 <= n <= 5,000 and 1 <= d <= 5,000. b and e are the beginning and ending positions for the desired range of digits, with 0 <= b,e <= 250 and 0 <= (e-b) <= 20. Note that 0 is the position immediately to the right of the decimal point.

Each problem set will be numbered (beginning at one) and will generate a single line:

Problem set k: n / d, base 7 digits b through e: result

where k is replaced by the problem set number, result is your computed result, and the other values are the corresponding input values.