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.math.BigInteger;
import java.util.*;
import static java.lang.Math.PI;
import static java.lang.System.in;
import static java.lang.System.out;

public class Main
{
    public static void main(String[] args) throws Exception
    {   
        Foster sc = new Foster();
        PrintWriter p = new PrintWriter(out);
        long n = sc.nextLong(), x = sc.nextLong(), m = sc.nextLong();
        long ans = 0;
        long cur = x;
        if(n <= 1000000)
        {
            for(int i = 0; i < n; i++)
            {
                ans +=  cur;
                long next = (cur*cur)%m;
                cur = next;
            }
        }
        else
        {
            ans = 0;
            long completed = n;
            cur = x;
            TreeSet<Long> tree = new TreeSet<>();
            for(int i = 0; i < 100000; i++)
            {
                if(tree.contains(cur))  break;
                ans += cur;
                tree.add(cur);
                long next = (cur*cur)%m;
                cur = next;
                completed--;
            }
            tree = new TreeSet<>();
            ArrayList<Long> repeat = new ArrayList<>();
            long sumofRepeat = 0;
            for(int i = 0; i < 1000000; i++)
            {
                if(tree.contains(cur))  break;
                sumofRepeat += cur;
                repeat.add(cur);
                tree.add(cur);
                long next = (cur*cur)%m;
                cur = next;
            }
            long inc = completed/tree.size();
            ans += sumofRepeat*inc;
            completed = completed%tree.size();
            for(long i : repeat)
            {
                if(completed==0)    break;
                ans += i;
                completed--;
            }
        }
        p.println(ans);
        p.close();
    }
/*

1000003 2 1001
1000003 2 16
*/    
/*
1. Check overflow in pow function or in general
2. Check indices of read array function
3. Think of an easier solution because the problems you solve are always easy
4. Check iterator of loop
5. If still doesn't work, then jump from the 729th floor 'coz "beta tumse na ho paayega"

    Move to top!!
*/

    static int[] sort(int[] a)
    {
        ArrayList<Integer> arr = new ArrayList<>();
        for(int i : a)
        {
            arr.add(i);
        }
        Collections.sort(arr);
        for(int i = 0 ; i < arr.size(); i++)
        {
            a[i] = arr.get(i);
        }
        return a;
    }
    
    static class Foster 
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(in));
        StringTokenizer st = new StringTokenizer("");
        String next() 
        {
            while (!st.hasMoreTokens())
                try 
                {
                    st = new StringTokenizer(br.readLine());
                } 
                catch (IOException e) 
                {
                    e.printStackTrace();
                }
            return st.nextToken();
        }
        int nextInt() 
        {
            return Integer.parseInt(next());
        }
        long nextLong() 
        {
            return Long.parseLong(next());
        }
        double nextDouble() 
        {
            return Double.parseDouble(next());
        }
        int[] intArray(int n)                   // Check indices
        {
            int arr[] = new int[n];
            for(int i = 0; i < n; i++)
            {
                arr[i] = nextInt();
            }
            return arr;
        }
        long[] longArray(int n)                 // Check indices
        {
            long arr[] = new long[n];
            for(int i = 0; i < n; i++)
            {
                arr[i] = nextLong();
            }
            return arr;
        }
        int[] getBits(int n)                    //in Reverse Order
        {
            int a[] = new int[31];
            for(int i = 0; i < 31; i++)
            {
                if(((1<<i) & n) != 0)
                    a[i] = 1;
            }
            return a;
        }
        static long pow(long... a)
        {
            long mod = Long.MAX_VALUE;
            if(a.length == 3)   mod = a[2];
            long res = 1;
            while(a[1] > 0)
            {
                if((a[1] & 1) == 1)
                    res = (res * a[0]) % mod;
                a[1] /= 2;
                a[0] = (a[0] * a[0]) % mod;
            }
            return res;
        }
        void print(Object... o) 
        {
            for(Object next : o)
            {
                System.err.print(next + " ");
            }
        }
        void println(Object... o) 
        {
            for(Object next : o)
            {
                System.err.print(next + " ");
            }
            System.err.println();
        }
        void watch(Object...a) throws Exception 
        {
            int i = 1;
            for (Object o: a) 
            {
                boolean found = false;
                if (o.getClass().isArray()) 
                {
                    String type = o.getClass().getName().toString();
                    switch (type) 
                    {
                        case "[I":
                        {
                            int[] test = (int[]) o;
                            println(i + " : " + Arrays.toString(test));
                            break;
                        }
                        case "[[I":
                        {
                            int[][] obj = (int[][]) o;
                            println(i + " : " + Arrays.deepToString(obj));
                            break;
                        }
                        case "[J":
                        {
                            long[] obj = (long[]) o;
                            println(i + " : " + Arrays.toString(obj));
                            break;
                        }
                        case "[[J":
                        {
                            long[][] obj = (long[][]) o;
                            println(i + " : " + Arrays.deepToString(obj));
                            break;
                        }
                        case "[D":
                        {
                            double[] obj = (double[]) o;
                            println(i + " : " + Arrays.toString(obj));
                            break;
                        }
                        case "[[D":
                        {
                            double[][] obj = (double[][]) o;
                            println(i + " : " + Arrays.deepToString(obj));
                            break;
                        }
                        case "[Ljava.lang.String":
                        {
                            String[] obj = (String[]) o;
                            println(i + " : " + Arrays.toString(obj));
                            break;
                        }
                        case "[[Ljava.lang.String":
                        {
                            String[][] obj = (String[][]) o;
                            println(i + " : " + Arrays.deepToString(obj));
                            break;
                        }
                        case "[C":
                        {
                            char[] obj = (char[]) o;
                            println(i + " : " + Arrays.toString(obj));
                            break;
                        }
                        case "[[C":
                        {
                            char[][] obj = (char[][]) o;
                            println(i + " : " + Arrays.deepToString(obj));
                            break;
                        }
                        default:
                        {
                            println(i + " : type not identified");
                            break;
                        }
                    }
                    found = true;
                }
                if (o.getClass() == ArrayList.class) 
                {
                    println(i + " : LIST = " + o);
                    found = true;
                }
                if (o.getClass() == TreeSet.class) 
                {
                    println(i + " : SET = " + o);
                    found = true;
                }
                if (o.getClass() == TreeMap.class) 
                {
                    println(i + " : MAP = " + o);
                    found = true;
                }
                if (o.getClass() == HashMap.class) 
                {
                    println(i + " : MAP = " + o);
                    found = true;
                }
                if (o.getClass() == LinkedList.class) 
                {
                    println(i + " : LIST = " + o);
                    found = true;
                }
                if (o.getClass() == PriorityQueue.class) 
                {
                    println(i + " : PQ = " + o);
                    found = true;
                }
                if (!found) 
                {
                    println(i + " = " + o);
                }
                i++;
            }
        }
    }
}