Problem:
Score : 500 points

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}.

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 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

Solution in PyPy3 (7.3.0) (judge verdict: Runtime Error)

N, X, M = map(int, input().split())
table = [0]*M

pre = X%M
table[pre] = 1
seq = [pre]
cnt = 0
while True:
    cnt += 1
    A = pre**2%M
    if not table[A]:
        seq.append(A)
        table[A] = cnt
        pre = A
    else:
        fir = table[A]
        sec = cnt
        break
    
ans = 0
for i in range(fir + (N-fir)%(sec-fir)):
    ans += seq[i]
mul = (N-fir)//(sec-fir)
for i in range(fir, sec):
    ans += seq[i]*mul

print(ans)