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 JavaScript (Node.js 12.16.1) (judge verdict: Time Limit Exceeded)

function Main(input) {
	const list = input.split(" ");
	const parse = a => parseInt(a.trim(), 10);
	const N = parse(list[0]);
	const X = parse(list[1]);
	const M = parse(list[2]);
	const rf = x => (x * x) % M;
	let tmp = rf(X);
	let ans = X;
	for(let i = 1;i < N; i++){
      	ans += tmp;
		tmp = rf(tmp);
	}
	console.log(ans);
};

Main(require("fs").readFileSync("/dev/stdin", "utf8"));