Problem Statement

Let us denote by f(x, m) the remainder of the Euclidean division of x by m.
Let A be the sequence that is defined by the initial value A_1=X and the recurrence relation A_{n+1} = f(A_n^2, M).
Find $\displaystyle{\sum_{i=1}^N A_i}$.

Input

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

Output

Print $\displaystyle{\sum_{i=1}^N A_i}$.

Constraints

• $1 \leq N \leq 10^{10}$
• $0 \leq X < M \leq 10^5$
• All values in input are integers.

Sample Input 1

6 2 1001

Sample Output 1

1369

The sequence $A begins 2,4,16,256,471,620,\ldots$ Therefore, the answer is 2+4+16+256+471+620=1369.

Sample Input 2

1000 2 16

Sample Output 2

6

The sequence $A begins 2,4,0,0,\ldots$ Therefore, the answer is 6.

Sample Input 3

10000000000 10 99959

Sample Output 3

492443256176507

见题面 Input 部分

见题面 Output 部分