Problem 43584. Find Pseudo-Cyclic Number

A cyclic number is an integer in which cyclic permutations of the digits are successive multiples of the number https://en.wikipedia.org/wiki/Cyclic_number>). The most widely known is 142857:

    142857 × 1 = 142857
    142857 × 2 = 285714
    142857 × 3 = 428571
    142857 × 4 = 571428
    142857 × 5 = 714285
    142857 × 6 = 857142 

In fact, 142857 is the only cyclic number in decimal, if leading zeros are not permitted on numerals.

Therefore, instead of the pure cyclic number, we will find the integer in which any cyclic permutations of the digits are any multiples of the number.

For example, 230769 is the one, because 23076 9 x 4 = 9 23076.

Given an integer x, return whether x is a pesudo-cyclic number.