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: Wrong Answer)

fun str() = readLine()!!
fun int() = str().toInt()
fun long() = str().toLong()

fun read(d: String = " ") = str().split(d)
fun <T> list(d: String = " ", f: String.() -> T) = read(d).map { f(it) }
fun list() = list { toInt() }

fun <T> MutableList<T>.removeLast() = this.removeAt(this.lastIndex)

//const val mod = 998244353L

fun main() {
    abc000X()
}

fun abc000X() {
    val (n, x, mod) = list { toLong() }


    var v = x
    var r = x

    val a = Array(mod.toInt()) { -1L to -1L }

    var i = 1L
    var f = true
    while (i < n) {
        ++i

        v = v * v % mod
        r += v

        if (f) {
            val (b, c) = a[v.toInt()]
            if (b < 0L) {
                a[v.toInt()] = i to r
            } else {
                f = false
                val l = (n - i + 1) / (i - b)
                val m = r - c

                r += l * m
                i += l * (i - b)
            }
        }
    }
    println(r)
}