CF303D Rotatable Number

Bike is a smart boy who loves math very much. He invented a number called "Rotatable Number" inspired by $ 142857 $ . As you can see, $ 142857 $ is a magic number because any of its rotatings can be got by multiplying that number by $ 1,2,...,6 $ (numbers from one to number's length). Rotating a number means putting its last several digit into first. For example, by rotating number $ 12345 $ you can obtain any numbers: $ 12345,51234,45123,34512,23451 $ . It's worth mentioning that leading-zeroes are allowed. So both $ 4500123 $ and $ 0123450 $ can be obtained by rotating $ 0012345 $ . You can see why $ 142857 $ satisfies the condition. All of the $ 6 $ equations are under base $ 10 $ . - $ 142857·1=142857 $ ; - $ 142857·2=285714 $ ; - $ 142857·3=428571 $ ; - $ 142857·4=571428 $ ; - $ 142857·5=714285 $ ; - $ 142857·6=857142 $ . Now, Bike has a problem. He extends "Rotatable Number" under any base $ b $ . As is mentioned above, $ 142857 $ is a "Rotatable Number" under base $ 10 $ . Another example is $ 0011 $ under base 2. All of the $ 4 $ equations are under base $ 2 $ . - $ 0011·1=0011 $ ; - $ 0011·10=0110 $ ; - $ 0011·11=1001 $ ; - $ 0011·100=1100 $ . So, he wants to find the largest $ b $ $ (1<b<x) $ so that there is a positive "Rotatable Number" (leading-zeroes allowed) of length $ n $ under base $ b $ . Note that any time you multiply a rotatable number by numbers from 1 to its length you should get a rotating of that number.

The only line contains two space-separated integers $ n,x $ $ (1

Print a single integer — the largest $ b $ you found. If no such $ b $ exists, print -1 instead.