// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;
#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::*;
#[allow(unused_imports)]
use std::f64::consts::*;

#[allow(unused)]
const INF: usize = std::usize::MAX / 4;
#[allow(unused)]
const M: usize = 1000000007;

fn inv(a: usize) -> usize {
    let m = M as i64;
    let mut a = a as i64;
    let mut b = m as i64;
    let mut u = 1;
    let mut v = 0;
    let mut tmp;
    while b != 0 {
        let t = a / b;
        a -= t * b;
        tmp = a;
        a = b;
        b = tmp;
        u -= t * v;
        tmp = u;
        u = v;
        v = tmp;
    }
    u %= m;
    if u < 0 {
        u += m;
    }
    return u as usize;
}

fn main() {
    input! {
        n: usize,
        m: usize,
        k: usize,
    }

    let mut f = vec![1; n * m + 1];
    let mut g = vec![1; n * m + 1];
    for i in 1..n * m + 1 {
        f[i] = i * f[i - 1] % M;
        g[i] = inv(f[i]);
    }

    let mut s = 0;
    for i in 1..=(n - 1) + (m - 1) {
        let fi = (f[n * m - 2] * g[k - 2] % M) * g[n * m - k] % M;
        let fi = i * fi % M;
        if n > i {
            let c = (n - i) * m % M;
            let si = c * fi % M;
            s = (s + si) % M;
        }
        if m > i {
            let c = n * (m - i) % M;
            let si = c * fi % M;
            s = (s + si) % M;
        }
        for j in if i > n { i - n } else { 0 } + 1..min(i, m) {
            if n + j > i && m > j {
                let c = 2 * (n + j - i) * (m - j) % M;
                let si = c * fi % M;
                s = (s + si) % M;
            }
        }
    }
    println!("{}", s);
}
*/

fn main() {
    let exe = "/tmp/bin8737D867";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "
f0VMRgIBAQAAAAAAAAAAAAIAPgABAAAAEANAAAAAAABAAAAAAAAAAGAiBAAAAAAAAAAAAEAAOAAGAEAA
DwAOAAEAAAAFAAAAAAAAAAAAAAAAAEAAAAAAAAAAQAAAAAAAQAIEAAAAAABAAgQAAAAAAAAAIAAAAAAA
AQAAAAYAAADACgQAAAAAAMAKZAAAAAAAwApkAAAAAAAYFwAAAAAAAGgyAAAAAAAAAAAgAAAAAAAHAAAA
BAAAAMAKBAAAAAAAwApkAAAAAADACmQAAAAAADAAAAAAAAAAyAAAAAAAAAAgAAAAAAAAAFDldGQEAAAA
LL8DAAAAAAAsv0MAAAAAACy/QwAAAAAANAkAAAAAAAA0CQAAAAAAAAQAAAAAAAAAUeV0ZAYAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEAAAAAAAAABS5XRkBAAAAMAKBAAAAAAA
wApkAAAAAADACmQAAAAAAEAVAAAAAAAAQBUAAAAAAAABAAAAAAAAAFBYwwAAAAAAAAAAAAAAAABBV0FW
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Measured memory_bytes: 8828