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 (a == 1) { IO.Printer.Out.WriteLine(1); return; } PreF.Add(1); for (int i = 1; true; i++) { var next = 1L; for (int j = 0; j < PreF[i - 1]; j++) { next *= a; if (next >= 100000) break; } if (next < 100000) PreF.Add(next); else break; } S = Enumerate(2048, x => -1); T = Enumerate(2048, x => -1); IO.Printer.Out.WriteLine(F(a, n, m)); } int[] S, T; List PreF = new List(); public long F(int a, int b, int m) { if (m == 1) return 0; if (b == 0) return 1; if (S[m] == -1) { var p = C(a, m); S[m] = p.Key; T[m] = p.Value; } if (b <= PreF.Count && PreF[b - 1] <= 100000) { var ret = ModPow(a, PreF[b - 1], m); return ret; } else { var res = F(a, b - 1, T[m]); return ModPow(a, S[m] + (res - S[m] + 1000 * T[m]) % T[m], m); } } public KeyValuePair C(int a, int mod) { a %= mod; var used = new int[mod]; for (int i = 0; i < mod; i++) used[i] = -1; var cur = 1; used[cur] = 0; while (true) { var next = (cur * a) % mod; if (used[next] == -1) used[next] = used[cur] + 1; else return new KeyValuePair(used[next], used[cur] + 1 - used[next]); cur = next; } } 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