Problem Description
There is a way of encryption in the Digital planet. If the number x, who lives in M area, K layer, then it will change its name to x ^ K mod M, that is newx = x ^ k mod m. Now the Digital Kingdom wants to make a program, which can find all the original number of a name living in some area, some layer. If there is no solution, output -1.
Input
There are multiply test cases. Each test case contains there integers k, m , newx ,(0 <= newx , m ,k <= 1.5*10^15) , m is a prime number.
Output
For each test case, you should output some lines, the format of the first line is: “caseN:” (N is the label of test case). Then next lines each contain a number x, output x as ascending order. (0 <= x < m)
Sample Input
1 5 4
2 13 8
3 13 8
Sample Output
case1:
4
case2:
-1
case3:
2
5
6
