Problem Statement

Among the sequences of length K consisting of integers, $A=(A_1, \ldots, A_K),$ how many satisfy all of the conditions below?
Find the count modulo 998244353.

• $0\leq A_i \leq M-1$ for every $i(1\leq i\leq K)$.

• $\displaystyle\prod_{i=1}^{K} A_i \equiv N \pmod M$.

Input

Input is given from Standard Input in the following format:
K N M

Output

Print the answer.

Constraints

• $1 \leq K \leq 10^9$
• $0 \leq N \lt M \leq 10^{12}$
• All values in input are integers.

Sample Input 1

2 3 6

Sample Output 1

5

The five sequences A satisfying the conditions are (1,3),(3,1),(3,3),(3,5),(5,3).

Sample Input 2

10 0 2

Sample Output 2

1023

Sample Input 3

1000000000 20220326 1000000000000

Sample Output 3

561382653

Be sure to find the count modulo 998244353.

见题面 Input 部分

见题面 Output 部分