using System;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Linq;

partial class Solver
{
    public void Run()
    {
        var N = ni();
        var M = ni();
        var K = ni();
        var mod = 1000000007;

        var C = new Binomial(N * M + 10, mod);
        long ans = 0;
        for (int d = 1; d < N; d++)
        {
            long w = N - d;
            ans += 1L * d * w % mod * M % mod * M % mod;
        }
        for (int d = 0; d < M; d++)
        {
            long w = M - d;
            ans += 1L * d * w % mod * N % mod * N % mod;
        }

        ans %= mod;
        ans *= C[N * M - 2, K - 2];
        ans %= mod;

        cout.WriteLine(ans);
    }
}


public class Binomial
{
    private readonly long[] factorial;
    private readonly long[] inverseFactorial;
    private readonly long[] inverse;
    private readonly int mod;

    public Binomial(int size, int primeMod)
    {
        size++;
        this.factorial = new long[size];
        this.inverseFactorial = new long[size];
        this.inverse = new long[size];
        this.mod = primeMod;
        Setup(size);
    }

    private void Setup(int size)
    {
        factorial[0] = factorial[1] = 1;
        inverseFactorial[0] = inverseFactorial[1] = 1;
        inverse[1] = 1;
        for (int i = 2; i < size; i++)
        {
            factorial[i] = factorial[i - 1] * i % mod;
            inverse[i] = (mod - (mod / i) * inverse[mod % i] % mod);
            inverseFactorial[i] = inverseFactorial[i - 1] * inverse[i] % mod;
        }
    }

    private long Get(int s, int t)
    {
        if (s < 0 || t < 0 || s < t) return 0;
        if (t == 0 || s == t) return 1;
        if (s >= mod) return Get(s % mod, t % mod) * Get(s / mod, t / mod) % mod; // Lucas' theorem
        return factorial[s] * inverseFactorial[t] % mod * inverseFactorial[s - t] % mod;
    }

    public long this[int s, int t]
    {
        get
        {
            return Get(s, t);
        }
    }

}
// 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<String> TokenQueue = new Queue<string>();
    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;
        }
    }
}


Measured memory_bytes: 15712