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 Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc, wr = bufio.NewScanner(os.Stdin), bufio.NewWriter(os.Stdout)

func scanString() string   { sc.Scan(); return sc.Text() }
func scanRunes() []rune    { return []rune(scanString()) }
func scanInt() int         { a, _ := strconv.Atoi(scanString()); return a }
func scanInt64() int64     { a, _ := strconv.ParseInt(scanString(), 10, 64); return a }
func scanFloat64() float64 { a, _ := strconv.ParseFloat(scanString(), 64); return a }

func scanInts(n int) []int {
	a := make([]int, n)
	for i := 0; i < n; i++ {
		a[i] = scanInt()
	}
	return a
}

func debug(a ...interface{}) {
	if os.Getenv("ONLINE_JUDGE") == "false" {
		fmt.Fprintln(os.Stderr, a...)
	}
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}
func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}
func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

//•*¨*•.¸¸♪main•*¨*•.¸¸♪(　-ω-)ノ　(　・ω・)
func main() {
	defer wr.Flush()
	sc.Split(bufio.ScanWords)
	sc.Buffer(make([]byte, 10000), 1001001)

	n, x, m := scanInt(), scanInt(), scanInt()
	u := make([]bool, m)
	a := []int{x}
	u[x] = true
	for i := 0; i < n; i++ {
		x = x * x % m
		if u[x] {
			break
		}
		u[x] = true
		a = append(a, x)
	}

	s := make([]int, len(a)+1)
	for i := 0; i < len(a); i++ {
		s[i+1] = s[i] + a[i]
	}

	ans := 0
	for i := 0; i < len(a); i++ {
		if a[i] == x {
			ans += (n / len(a[i:])) * (s[len(a)] - s[i])
			n -= n / len(a[i:]) * len(a[i:])
			if n == 0 {
				break
			}
		}
		ans += a[i]
		n--
		if n == 0 {
			break
		}
	}

	fmt.Fprintln(wr, ans)

}