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 Kotlin (1.3.71) (judge verdict: Time Limit Exceeded)

fun main(args: Array<String>) {
    val (N, X, M) = readLine()!!.split(' ').map { it.toLong() }
    var x = X
    var cnt = 1L
    var ans = 0L
    val f = mutableSetOf<Long>()
    val loopArr = LongArray(M.toInt()+1)
    var loopTop = -1L
    var loopIn = false
    var loopSum = 0L
    var loopLen = 0L

    while(cnt <= N && !loopIn) {
        val next = x*x
        if (f.find{ it == x} != null) {
            loopIn = true
            loopTop = x
            loopArr[loopLen.toInt()] = x
            loopSum += x
            loopLen++
        }
        f.add(x)
        ans += x
        x = next % M
        cnt++
    }
    if (x == 0L) {
        println(ans)
        return
    }

    while (cnt <= N && x != loopTop) {
        ans += x
        loopArr[loopLen.toInt()] = x
        loopSum += x
        loopLen++
        x = (x * x) % M
        cnt++
    }
    if (loopLen > 0) {
        val loops = (N - cnt) / loopLen
        ans += loopSum * loops
        cnt += loopLen * loops

        var cnt2 = 0
        while (cnt <= N) {
            ans += loopArr[cnt2]
            cnt++
            cnt2++
        }
    }

    println(ans)
}