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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.
Input: 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.
Output: 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.
| Example input: | Example output: |
| 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 |