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 $A_{n+1} = f(A_n^2, M). Find \displaystyle{\sum_{i=1}^N A_i}$.

Constraints

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

Input

Input is given from Standard Input in the following format:

N X M

Output

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

Examples

Input

6 2 1001

Output

1369

Input

1000 2 16

Output

6

Input

10000000000 10 99959

Output

492443256176507

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见题面