using System; using System.Linq; using System.Linq.Expressions; using System.Collections.Generic; using Debug = System.Diagnostics.Debug; using StringBuilder = System.Text.StringBuilder; using System.Numerics; using Point = System.Numerics.Complex; using Number = System.Int32; namespace Program { public class Solver { public void Solve() { var a = sc.Integer(); var n = sc.Integer(); var m = sc.Integer(); if (m == 1) { IO.Printer.Out.WriteLine(0); return; } if (n == 0) { IO.Printer.Out.WriteLine(1); return; } n--; var phi = MathEx.EulerTotient(m); var used = new int[phi + 1]; for (int i = 0; i <= phi; i++) used[i] = -1; used[1] = 0; var cur = 1L; var T = 0L; while (true) { var next = ModPow(a, cur, phi); if (used[next] == -1) { used[next] = used[cur] + 1; } else { T = used[cur] + 1 - used[next]; break; } cur = next; } Debug.WriteLine(phi); Debug.WriteLine(T); for (int i = 0; i <= phi; i++) { if (n <= used[cur]) { if (used[i] == n) { IO.Printer.Out.WriteLine(ModPow(a, i, m)); return; } } else { if (used[i] < used[cur]) continue; if ((n - used[i]) % T == 0) { IO.Printer.Out.WriteLine(ModPow(a, i, m)); } } } } static public long ModPow(long x, long n, long mod) { long r = 1; while (n > 0) { if ((n & 1) == 1) r = r * x % mod; x = x * x % mod; n >>= 1; } return r; } public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput()); static T[] Enumerate(int n, Func f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(i); return a; } static public void Swap(ref T a, ref T b) { var tmp = a; a = b; b = tmp; } } } #region main static class Ex { static public string AsString(this IEnumerable ie) { return new string(System.Linq.Enumerable.ToArray(ie)); } static public string AsJoinedString(this IEnumerable ie, string st = " ") { return string.Join(st, ie); } static public void Main() { var solver = new Program.Solver(); solver.Solve(); Program.IO.Printer.Out.Flush(); } } #endregion #region Ex namespace Program.IO { using System.IO; using System.Text; using System.Globalization; public class Printer : StreamWriter { static Printer() { Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false }; } public static Printer Out { get; set; } public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } } public Printer(System.IO.Stream stream) : base(stream, new UTF8Encoding(false, true)) { } public Printer(System.IO.Stream stream, Encoding encoding) : base(stream, encoding) { } public void Write(string format, T[] source) { base.Write(format, source.OfType().ToArray()); } public void WriteLine(string format, T[] source) { base.WriteLine(format, source.OfType().ToArray()); } } public class StreamScanner { public StreamScanner(Stream stream) { str = stream; } public readonly Stream str; private readonly byte[] buf = new byte[1024]; private int len, ptr; public bool isEof = false; public bool IsEndOfStream { get { return isEof; } } private byte read() { if (isEof) return 0; if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; } } return buf[ptr++]; } public char Char() { byte b = 0; do b = read(); while ((b < 33 || 126 < b) && !isEof); return (char)b; } public string Scan() { var sb = new StringBuilder(); for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b); return sb.ToString(); } public string ScanLine() { var sb = new StringBuilder(); for (var b = Char(); b != '\n'; b = (char)read()) if (b == 0) break; else if (b != '\r') sb.Append(b); return sb.ToString(); } public long Long() { if (isEof) return long.MinValue; long ret = 0; byte b = 0; var ng = false; do b = read(); while (b != 0 && b != '-' && (b < '0' || '9' < b)); if (b == 0) return long.MinValue; if (b == '-') { ng = true; b = read(); } for (; true; b = read()) { if (b < '0' || '9' < b) return ng ? -ret : ret; else ret = ret * 10 + b - '0'; } } public int Integer() { return (isEof) ? int.MinValue : (int)Long(); } public double Double() { var s = Scan(); return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN; } private T[] enumerate(int n, Func f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(); return a; } public char[] Char(int n) { return enumerate(n, Char); } public string[] Scan(int n) { return enumerate(n, Scan); } public double[] Double(int n) { return enumerate(n, Double); } public int[] Integer(int n) { return enumerate(n, Integer); } public long[] Long(int n) { return enumerate(n, Long); } } } #endregion #region Totient public static partial class MathEx { /// Return phi(n) public static long EulerTotient(long n) { var res = n; for (int i = 2; i * i <= n; i++) { if (n % i == 0) { res = res / i * (i - 1); for (; n % i == 0; n /= i) ; } } if (n != 1) res = res / n * (n - 1); return res; } /// Return phi(n)'s table public static int[] EulerTotientSieve(int n) { var res = new int[n]; for (int i = 0; i < n; i++) res[i] = i; for (int i = 2; i < n; i++) if (res[i] == i) for (int j = i; j < n; j += i) res[j] = res[j] / i * (i - 1); return res; } } #endregion