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

-----Sample Input-----
6 2 1001

-----Sample Output-----
1369

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

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