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: Runtime Error)

fun main() {
    val inputs = readLine()!!.split(" ")
    val n = inputs[0].toLong()
    var x = inputs[1].toLong()
    val m = inputs[2].toLong()

    val num = HashMap<Long, Int>()
    val sum = mutableListOf<Long>(0)

    num[x] = 0
    sum.add(x)
    var cnt = 2
    while (cnt <= m+1) {
        x = f(x, m)
        sum.add(sum[cnt - 1] + x)
        if (!num.containsKey(x)) {
            num[x] = cnt
        } else {
            break
        }
        cnt += 1
    }

    val len = cnt - num[x]!!
    val first = if (n > cnt) sum[cnt - len - 1] else sum[n.toInt()]
    if (n <= cnt) {
        println(first)
    } else {
        val middleLen = (n - (cnt - len - 1)) / len.toLong()
        val middle = (sum[cnt-1] - sum[num[x]!!-1]) * middleLen
        val endLen = (n - (cnt - len - 1)) % len
        val end = sum[num[x]!! - 1 + endLen.toInt()] - sum[num[x]!! - 1]

        println(first + middle + end)
    }
}

fun f(x: Long, mod: Long): Long {
    return (x * x) % mod
}