using System;
using System.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
using System.Numerics;
using System.Runtime.InteropServices.ComTypes;
using System.Xml.Schema;
using System.ComponentModel.DataAnnotations;
using System.Security.Cryptography;
using System.Drawing;
using System.Runtime.CompilerServices;

namespace AtCoder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
            Solve();
            //Out.Flush();
            Read();
        }

        static void Solve()
        {
            var (N, M, K) = Slice3<long>();
            var cmb = new Combination(N * M + 1, Mod);
            var cmnY = M * M % Mod * cmb.nCk((int)(M * N - 2), (int)K - 2) % Mod;
            var numY = 0L;
            for (var i = 1L; i < N; ++i)
                numY = (numY + i * (N - i) % Mod) % Mod;
            numY = numY * cmnY % Mod;
            var cmnX = N * N % Mod * cmb.nCk((int)(M * N - 2), (int)K - 2) % Mod;
            var numX = 0L;
            for (var i = 1L; i < M; ++i)
                numX = (numX + i * (M - i) % Mod) % Mod;
            numX = numX * cmnX % Mod;
            WriteLine((numY + numX) % Mod);
        }
        public class Combination
        {
            readonly long mod;
            readonly long[] fac, finv, inv;
            public Combination(long n, long mod = 1000000007)
            {
                long max = n + 1;
                this.mod = mod;
                fac = new long[max];
                finv = new long[max];
                inv = new long[max];
                fac[0] = fac[1] = 1;
                finv[0] = finv[1] = 1;
                inv[1] = 1;
                for (int i = 2; i < max; ++i)
                {
                    fac[i] = fac[i - 1] * i % mod;
                    inv[i] = mod - inv[mod % i] * (mod / i) % mod;
                    finv[i] = finv[i - 1] * inv[i] % mod;
                }
            }
            public long nCk(int n, int k)
            {
                if (n < k) return 0;
                if (n < 0 | k < 0) return 0;
                return fac[n] * (finv[k] * finv[n - k] % mod) % mod;
            }
        }

        static long Mod = (long)1e9 + 7;
        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }
        static public (T1 a, T2 b) Slice<T1, T2>()
        {
            var t = ReadLine().Split();
            return (
            (T1)Convert.ChangeType(t[0], typeof(T1)),
            (T2)Convert.ChangeType(t[1], typeof(T2)));
        }
        static public (T a, T b) Slice2<T>()
        {
            var t = ReadLine().Split();
            return (
            (T)Convert.ChangeType(t[0], typeof(T)),
            (T)Convert.ChangeType(t[1], typeof(T)));
        }
        static public (T a, T b, T c) Slice3<T>()
        {
            var t = ReadLine().Split();
            return (
            (T)Convert.ChangeType(t[0], typeof(T)),
            (T)Convert.ChangeType(t[1], typeof(T)),
            (T)Convert.ChangeType(t[2], typeof(T)));
        }
        static public (T a, T b, T c, T d) Slice4<T>()
        {
            var t = ReadLine().Split();
            return (
            (T)Convert.ChangeType(t[0], typeof(T)),
            (T)Convert.ChangeType(t[1], typeof(T)),
            (T)Convert.ChangeType(t[2], typeof(T)),
            (T)Convert.ChangeType(t[3], typeof(T)));
        }
    }
}

Measured memory_bytes: 32568