#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        #[cfg(debug_assertions)]
        writeln!(&mut std::io::stderr(), concat!("[DEBUG] ", $(stringify!($a), "={:?} "),*), $($a),*);
    }
}

#[allow(unused_imports)]
use std::cmp::{min, max};

#[allow(unused_imports)]
use std::io::Write;
const MAX: usize = 1e5 as usize * 2 + 1;
const MOD: usize = 1e9 as usize + 7;

#[allow(dead_code)]
pub struct ModDivision {
    fact: Vec<usize>,
    inv: Vec<usize>,
    finv: Vec<usize>,
}
impl ModDivision {
    pub fn new(max_value: usize) -> Self {
        let mut fact = vec![0; max_value + 1];
        let mut inv = vec![0; max_value + 1];
        let mut finv = vec![0; max_value + 1];
        fact[0] = 1;
        fact[1] = 1;
        finv[0] = 1;
        finv[1] = 1;
        inv[1] = 1;
        for i in 2..max_value + 1 {
            fact[i] = fact[i - 1] * i % MOD;
            inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
            finv[i] = finv[i - 1] * inv[i] % MOD;
        }
        ModDivision {
            fact: fact,
            inv: inv,
            finv: finv,
        }
    }
    pub fn combination(&self, n: usize, k: usize) -> usize {
        assert!(n >= k);
        self.fact[n] * self.finv[n - k] % MOD * self.finv[k] % MOD
    }
}

fn main() {
    input!{
      n: usize,
      m: usize,
      k: usize,
    }
    let mut ans = 0;
    let div = ModDivision::new(MAX);
    let pair = div.combination(n*m-2,k-2);
    for d in 1..m {
        ans += n*n*(m-d)*d%MOD *pair%MOD;
        ans %= MOD;
    }
    for d in 1..n {
        ans += m*m*(n-d)*d%MOD *pair%MOD;
        ans %= MOD;
    }
    println!("{}", ans);
}


Measured memory_bytes: 10492