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.*;

public class Main{
	static void main() throws Exception{
		long n=sc.nextLong();
		int x=sc.nextInt(),m=sc.nextInt();
		if(m==1) {
			pw.println(0);
			return;
		}
		int[]seen=new int[m];
		Arrays.fill(seen, -1);
		int cur=x;
		int cnt=0;
		long sum=0;
		long[]sums=new long[m];
		while(seen[cur]==-1 && cnt<n) {
			seen[cur]=cnt;
			sum+=cur;
			sums[cnt]=sum;
			cnt++;
			cur=(int)((cur*1l*cur)%m);
		}
		if(cnt==n || cur==0) {
			pw.println(sum);
			return;
		}
		int cycle=cnt-seen[cur];
		int notCycle=cnt-cycle;
		long sumNotCycle=seen[cur]==0?0:sums[seen[cur]-1];
//		System.out.println(cnt+" "+seen[cur]+" "+cur+" "+notCycle+" "+cycle+" "+sumNotCycle);
		n-=notCycle;
		sum-=sumNotCycle;
		long ans=(n/cycle)*sum;
		long rem=n%cycle;
		while(rem>0) {
			ans+=cur;
			rem--;
			cur=(int)((cur*1l*cur)%m);
		}
		pw.println(ans+sumNotCycle);
	}
	public static void main(String[] args) throws Exception {
		sc = new MScanner(System.in);
		pw = new PrintWriter(System.out);
//		int tc = 1;
//		tc=sc.nextInt();
//		while (tc-- > 0)
			main();
		pw.flush();
	}

	static PrintWriter pw;
	static MScanner sc;

	static class MScanner {
		StringTokenizer st;
		BufferedReader br;

		public MScanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public MScanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int[] intArr(int n) throws IOException {
			int[] in = new int[n];
			for (int i = 0; i < n; i++)
				in[i] = nextInt();
			return in;
		}

		public long[] longArr(int n) throws IOException {
			long[] in = new long[n];
			for (int i = 0; i < n; i++)
				in[i] = nextLong();
			return in;
		}

		public int[] intSortedArr(int n) throws IOException {
			int[] in = new int[n];
			for (int i = 0; i < n; i++)
				in[i] = nextInt();
			shuffle(in);
			Arrays.sort(in);
			return in;
		}

		public long[] longSortedArr(int n) throws IOException {
			long[] in = new long[n];
			for (int i = 0; i < n; i++)
				in[i] = nextLong();
			shuffle(in);
			Arrays.sort(in);
			return in;
		}

		public Integer[] IntegerArr(int n) throws IOException {
			Integer[] in = new Integer[n];
			for (int i = 0; i < n; i++)
				in[i] = nextInt();
			return in;
		}

		public Long[] LongArr(int n) throws IOException {
			Long[] in = new Long[n];
			for (int i = 0; i < n; i++)
				in[i] = nextLong();
			return in;
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}

	static void shuffle(int[] in) {
		for (int i = 0; i < in.length; i++) {
			int idx = (int) (Math.random() * (i + 1));
			int tmp = in[i];
			in[i] = in[idx];
			in[idx] = tmp;
		}
	}

	static void shuffle(long[] in) {
		for (int i = 0; i < in.length; i++) {
			int idx = (int) (Math.random() * (i + 1));
			long tmp = in[i];
			in[i] = in[idx];
			in[idx] = tmp;
		}
	}
}