#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::fs::File;
#[allow(unused_imports)]
use std::io::prelude::*;
#[allow(unused_imports)]
use std::io::Stdin;
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufReader, BufWriter, Write};
#[allow(unused_imports)]
use std::mem::swap;
#[allow(unused_imports)]
use std::str::FromStr;

type BoxResult<T> = Result<T, Box<std::error::Error>>;

fn main() {
    let mut scanner = Scanner::new(stdin());
    let param = scanner.read_vector::<u64>().unwrap();
    let (n, m, k) = (param[0], param[1], param[2]);
    let modulo = 1_000_000_000 + 7;
    let mut ans = 0;
    for i in 1..n {
        ans = (ans + (((((n - i) * m) % modulo) * m * i) % modulo)) % modulo;
    }
    for i in 1..m {
        ans = (ans + (((((m - i) * n) % modulo) * n * i) % modulo)) % modulo;
    }
    ans = (ans * combination(n * m - 2, k - 2, modulo)) % modulo;
    println!("{}", ans);
}

fn combination(n: u64, k: u64, modulo: u64) -> u64 {
    if k == 0 {
        return 1;
    }
    let n_fact = factorial(n, modulo);
    let k_fact = factorial(k, modulo);
    let nk_fact = factorial(n - k, modulo);
    let k_pow_inv = pow(k_fact, modulo - 2, modulo);
    let nk_pow_inv = pow(nk_fact, modulo - 2, modulo);
    let mut ans = n_fact;
    ans = (ans * k_pow_inv) % modulo;
    ans = (ans * nk_pow_inv) % modulo;
    ans
}

fn factorial(n: u64, modulo: u64) -> u64 {
    let mut n_fact = 1;
    for i in 2..(n + 1) {
        n_fact = (n_fact * i) % modulo;
    }
    n_fact
}

fn pow(x: u64, mut n: u64, modulo: u64) -> u64 {
    let mut pows = vec![x];
    for i in 0..63 {
        let square = (pows[i] * pows[i]) % modulo;
        pows.push(square);
    }
    let mut ans = 1;
    for i in 0..64 {
        let flag = n & 1;
        n >>= 1;
        if flag == 1 {
            ans = (ans * pows[i]) % modulo;
        }
    }
    ans
}

#[allow(dead_code)]
struct Scanner<R> {
    reader: BufReader<R>,
    buffer: String,
}

impl<R> Scanner<R>
where
    R: Read,
{
    #[allow(dead_code)]
    fn new(inner: R) -> Scanner<R> {
        let reader = BufReader::new(inner);
        let buffer = String::new();
        Scanner { reader: reader, buffer: buffer }
    }

    #[allow(dead_code)]
    fn with_capacity(capacity: usize, inner: R) -> Scanner<R> {
        let reader = BufReader::with_capacity(capacity, inner);
        let buffer = String::new();
        Scanner { reader: reader, buffer: buffer }
    }

    #[allow(dead_code)]
    fn read<T>(&mut self) -> BoxResult<T>
    where
        T: FromStr,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let parsed = self.buffer.trim().parse()?;
        self.buffer.clear();
        Ok(parsed)
    }

    #[allow(dead_code)]
    fn read_vector<T>(&mut self) -> BoxResult<Vec<T>>
    where
        T: FromStr,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let parsed_vec = self
            .buffer
            .trim()
            .split_whitespace()
            .map(|s| s.parse())
            .collect::<Result<Vec<_>, _>>()?;
        self.buffer.clear();
        Ok(parsed_vec)
    }

    #[allow(dead_code)]
    fn read_matrix<T>(&mut self, lines: usize) -> BoxResult<Vec<Vec<T>>>
    where
        T: FromStr,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        let mut parsed_matrix = vec![];
        for _ in 0..lines {
            self.reader.read_line(&mut self.buffer)?;
            parsed_matrix.push(
                self.buffer
                    .trim()
                    .split_whitespace()
                    .map(|s| s.parse())
                    .collect::<Result<Vec<_>, _>>()?,
            );
            self.buffer.clear();
        }
        Ok(parsed_matrix)
    }
}



Measured memory_bytes: 4352