using System; using System.IO; using System.Collections.Generic; using System.Globalization; using System.Linq; using System.Text; using System.Numerics; partial class Solver { static public long Gcd(long s, long t) { return t != 0 ? Gcd(t, s % t) : s; } static public long Lcm(long s, long t) { return s / Gcd(s, t) * t; } static public List Divisors(int x) { List ret = new List(); for (int i = 1; i * i <= x; i++) { if (x % i == 0) { ret.Add(i); if (i != x / i) ret.Add(x / i); } } ret.Sort(); return ret; } static Dictionary memo = new Dictionary(); static public long Phi(long n) { if (memo.ContainsKey(n)) return memo[n]; var nn = n; long phi = n; for (long i = 2; i * i <= n && i < n; i++) { if (n % i == 0) { while (n % i == 0) n /= i; phi = phi / i * (i - 1); } } if (n > 1) phi = phi / n * (n - 1); return memo[nn] = phi; } static public long ExtendedGcd(long a, long b, ref long x, ref long y) { if (b == 0) { x = 1; y = 0; return a; } else { long d = ExtendedGcd(b, a % b, ref y, ref x); y -= a / b * x; return d; } } static public long Inverse(long a, long mod) { long x = 0, y = 0; if (ExtendedGcd(a, mod, ref x, ref y) == 1) return (x + mod) % mod; else return -1; } static public long ModPow(long x, long n, long mod) { x %= mod; if (n == 0) return 1; else if (n % 2 != 0) return x * ModPow(x, n - 1, mod) % mod; else return ModPow((x * x) % mod, n / 2, mod); } public void Run() { var H = ni(); var W = ni(); var K = ni(); const int mod = 1000000007; var dH = Divisors(H); var dW = Divisors(W); long ans = 0; foreach (var h in dH) { foreach (var w in dW) { ans += (long)(Phi(h) * Phi(w) % mod * ModPow(K, 1L * W * H / w / h * Gcd(w, h), mod) % mod); ans %= mod; } } ans = (ans * Inverse(1L * W * H, mod)) % mod; cout.WriteLine(ans); } } // PREWRITEN CODE BEGINS FROM HERE partial class Solver : Scanner { public static void Main(string[] args) { new Solver(Console.In, Console.Out).Run(); } TextReader cin; TextWriter cout; public Solver(TextReader reader, TextWriter writer) : base(reader) { this.cin = reader; this.cout = writer; } public Solver(string input, TextWriter writer) : this(new StringReader(input), writer) { } public int ni() { return NextInt(); } public int[] ni(int n) { return NextIntArray(n); } public long nl() { return NextLong(); } public long[] nl(int n) { return NextLongArray(n); } public double nd() { return NextDouble(); } public string ns() { return Next(); } } public class Scanner { private TextReader Reader; private Queue TokenQueue = new Queue(); private CultureInfo ci = CultureInfo.InvariantCulture; public Scanner() : this(Console.In) { } public Scanner(TextReader reader) { this.Reader = reader; } public int NextInt() { return Int32.Parse(Next(), ci); } public long NextLong() { return Int64.Parse(Next(), ci); } public double NextDouble() { return double.Parse(Next(), ci); } public string[] NextArray(int size) { var array = new string[size]; for (int i = 0; i < size; i++) array[i] = Next(); return array; } public int[] NextIntArray(int size) { var array = new int[size]; for (int i = 0; i < size; i++) array[i] = NextInt(); return array; } public long[] NextLongArray(int size) { var array = new long[size]; for (int i = 0; i < size; i++) array[i] = NextLong(); return array; } public String Next() { if (TokenQueue.Count == 0) { if (!StockTokens()) throw new InvalidOperationException(); } return TokenQueue.Dequeue(); } public bool HasNext() { if (TokenQueue.Count > 0) return true; return StockTokens(); } private bool StockTokens() { while (true) { var line = Reader.ReadLine(); if (line == null) return false; var tokens = line.Trim().Split(" ".ToCharArray(), StringSplitOptions.RemoveEmptyEntries); if (tokens.Length == 0) continue; foreach (var token in tokens) TokenQueue.Enqueue(token); return true; } } }