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}.

Examples

Input

6 2 1001


Output

1369


Input

1000 2 16


Output

6


Input

10000000000 10 99959


Output

492443256176507
import java.io.*;
import java.util.*;

class Main {
	public static void main(String[] $) {
		new Main().run();
	}
	
	void run() {
		Scanner sc=new Scanner(System.in);
		long N=sc.nextLong();
		long X=sc.nextLong();
		long M=sc.nextLong();
		long ans=0;
		int[] vis=new int[(int)M];
		long[] pre=new long[(int)M];
		Arrays.fill(vis, -1);
		int p=0;
		while (N-->0) {
			vis[(int)X]=p++;
			pre[(int)X]=ans;
			ans+=X;
			X=X*X%M;
			if (vis[(int)X]!=-1) {
				int T=p-vis[(int)X];
				ans+=N/T*(ans-pre[(int)X]);
				N%=T;
			}
		}
		System.out.println(ans);
	}
	
	void tr(Object...objects) {System.out.println(Arrays.deepToString(objects));}
}
