Multiplying by Rotation
| Program |
MULTIPLY.C MULTIPLY.CPP MULTIPLY.PAS |
Multiplication of natural numbers in general is a cumbersome operation. In
some cases however the product can be obtained by moving the last digit to the
front.
Example: 179487 * 4 = 717948
Of course this property depends on the number system you use, in the above example
we used the decimal representation. In base 9 we have a shorter example:
17 * 4 = 71 (base 9)
as (9 * 1 + 7) * 4 = 7 * 9 + 1
Input
The input for your program is a textfile. Each line consists of three numbers
separated by a space: the base of the number system, the least significant digit
of the first factor, and the second factor. This second factor is one digit
only hence less than the base. The base is less than or equal to 10. The input
file ends with the standard end-of-file marker.
Output
Your program determines for each input line the smallest first factor with the
rotamult property. The output-file is also a textfile. Each line contains the
answer for the corresponding input line.
Sample Input
10 7 4
9 7 4
7 4 2
Sample Output
179487
17
210352456314