Cyclic Numbers
시간 제한1초메모리 제한512 MB
1000자리 이하의 정수가 주어질 때, 1부터 자릿수까지의 모든 배수가 원래 숫자의 회전인지 판별합니다.
문제
A cyclic number is a positive integer n digits in length which, when multiplied by any integer from 1 to n, yields a "cycle" of the digits of the original number. That is, if you consider the number after the last digit to "wrap around" back to the first digit, the sequence of digits in both numbers will be the same, though they may start at different positions.
For example, the number 142857 is cyclic, as illustrated by the following table:
- 142857 × 1 = 142857
- 142857 × 2 = 285714
- 142857 × 3 = 428571
- 142857 × 4 = 571428
- 142857 × 5 = 714285
- 142857 × 6 = 857142
Write a program which will determine whether or not numbers are cyclic.
입력
The input is a list of integers from 2 to 1000 digits in length (preceding zeroes are legal).
출력
In the output, display each integer and indicate whether or not it is cyclic.