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
N,X,M = map(int,input().split())
ls = [X]
for i in range(M):
    Ai = ls[-1]**2 % M
    if Ai in ls:
        loop = ls[ls.index(Ai):]
        lenloop = len(loop)
        sumloop = sum(loop)
        startls = ls[:ls.index(Ai)]
        break
    ls.append(Ai)
if N <= len(startls):
    ans = sum(startls[:N])
else:
    ans = sum(startls) + ((N-len(startls))//lenloop)*sumloop + sum(loop[:(N-len(startls))%lenloop])
print(ans)
