
Score : 1400 points
Problem StatementProcess the Q queries below.
You are given two integers A_i and M_i. Determine whether there exists a positive integer K_i not exceeding 2 × 10^{18} such that A_i^{K_i} ≡ K_i (mod M_i), and find one if it exists.
Constraints
1 \leq Q \leq 100
0 \leq A_i \leq 10^9(1 \leq i \leq Q)
1 \leq M_i \leq 10^9(1 \leq i \leq Q)
InputsInput is given from Standard Input in the following format:
Q
A_1 M_1
:
A_Q M_Q
OutputsIn the i-th line, print -1 if there is no integer K_i that satisfies the condition.
Otherwise, print an integer K_i not exceeding 2 × 10^{18} such that A_i^{K_i} ≡ K_i (mod M_i). If there are multiple solutions, any of them will be accepted.
Sample Input 14
2 4
3 8
9 6
10 7
Sample Output 14
11
9
2
It can be seen that the condition is satisfied: 2^4 = 16 ≡ 4 (mod 4), 3^{11} = 177147 ≡ 11 (mod 8), 9^9 = 387420489 ≡ 9 (mod 6) and 10^2 = 100 ≡ 2 (mod 7).
Sample Input 23
177 168
2028 88772
123456789 987654321
Sample Output 27953
234831584
471523108231963269
