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 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.

4
1 5 0 0
6 49 1 3
33 4 2 7
511 977 122 126

Problem set 1: 1 / 5, base 7 digits 0 through 0: 1
Problem set 2: 6 / 49, base 7 digits 1 through 3: 600
Problem set 3: 33 / 4, base 7 digits 2 through 7: 151515
Problem set 4: 511 / 977, base 7 digits 122 through 126: 12425

Mid-Central USA 2005