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)

import sys
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

N, X, mod = mapint()

s = set()
s.add(X)
s_loop = set()
ans = X
loop = 0
loops = []
for i in range(min(10**5*2+10, N-1)):
    X = pow(X, 2, mod)
    if X in s:
        if X in s_loop:
            loops.append(X)
            break
        loop += X
        s_loop.add(X)
        loops.append(X)
    s.add(X)
    ans += X

rest = N-i-2
if rest:
    ans += (rest//len(s_loop))*loop
    amari = rest%len(s_loop)+1
    for i in range(amari):
        ans += loops[i]
    print(ans)
else:
    print(ans)