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())
al = []
result= x
for i in range(1, n):
    temp = pow(x, 2**i)
    if(m <= temp):
        break
    else:
        result+=temp
for j in range(i, n):
    temp2 = pow(x, 2**j, m)
    if(len(al) > 0):
        if(al[0] == temp2):
            suma = sum(al)
            print(al)
            result += suma * (n-i)//(j - i)
            for k in range(0, (n-i)%(j-i)):
                result+=al[k]
            break
    al.append(temp2)
else:
    result += sum(al)
    
print(result)