A square root of a number x is a number r such that r2 = x. A discrete square root of a non-negative integerxisanon-negativeintegerrsuchthatr2 ≡xmodN,0≤r<N,whereNisaspecific positive integer and mod is the modulo operation. It is well-known that any positive real number has exactly two square roots, but a non-negative integer may have more than two discrete square roots. For example, for N = 12, 1 has four discrete square roots 1, 5, 7 and 11. Your task is to find all discrete square roots of a given non-negative integer x. To make it easier, a known square root r of x is also given to you. Input The input consists of multiple test cases. Each test case contains exactly one line, which gives three integers x, N and r. (1 ≤ x < N, 2 ≤ N < 1,000,000,000, 1 ≤ r < N). It is guaranteed that r is a discrete square root of x modulo N. The last test case is followed by a line containing three zeros. Output For each test case, print a line containing the test case number (beginning with 1) followed by a list of corresponding discrete square roots, in which all numbers are sorted increasingly. Sample Input 1 12 1 4 15 2 000 Sample Output Case 1: 1 5 7 11 Case 2: 2 7 8 13