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 Julia (1.4.0) (judge verdict: Runtime Error)

parseline(str=readline()) = parse.(Int, split(str))
function main()
    N, X, M = parseline()
    ans = 0
    temp = X
    A = zeros(Int, M+1)
    for m in 1:M+1
        A[m] = temp
        temp = powermod(temp, 2, M)
        temp ≡ 0 && break
        if temp ≡ 1
            A[m:end] .= 1
            break
        end
    end
    for n in 1:N
        ans += A[mod(n, M)]
    end
    println(ans)
end
main()