// 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::*;

type Mint = kyopro_lib::modint::Mint1_000_000_007;

fn main() {
    input! {
        n: u64,
        m: u64,
        k: u64,
    }

    let (pos, neg) = Mint::gen_factorial(n * m);
    let binomial = |n, r| pos[n as usize] * neg[r as usize] * neg[(n - r) as usize];

    let mut res = Mint::new(0);
    for d in 1..n {
        res += Mint::new(d) * binomial(n * m - 2, k - 2) * Mint::new((n - d) * m * m);
    }
    for d in 1..m {
        res += Mint::new(d) * binomial(n * m - 2, k - 2) * Mint::new((m - d) * n * n);
    }
    println!("{}", res.val());
}
*/

fn main() {
    let exe = "/tmp/binFB9332E7";
    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 = "
f0VMRgIBAQAAAAAAAAAAAAIAPgABAAAAYANAAAAAAABAAAAAAAAAAHCCAwAAAAAAAAAAAEAAOAAHAEAA
EAAPAAEAAAAFAAAAAAAAAAAAAAAAAEAAAAAAAAAAQAAAAAAAYGADAAAAAABgYAMAAAAAAAAAIAAAAAAA
AQAAAAYAAABAagMAAAAAAEBqYwAAAAAAQGpjAAAAAACYFwAAAAAAAOgyAAAAAAAAAAAgAAAAAAAEAAAA
BAAAAMgBAAAAAAAAyAFAAAAAAADIAUAAAAAAACQAAAAAAAAAJAAAAAAAAAAEAAAAAAAAAAcAAAAEAAAA
QGoDAAAAAABAamMAAAAAAEBqYwAAAAAAMAAAAAAAAADIAAAAAAAAACAAAAAAAAAAUOV0ZAQAAACMGwMA
AAAAAIwbQwAAAAAAjBtDAAAAAADMCQAAAAAAAMwJAAAAAAAABAAAAAAAAABR5XRkBgAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQAAAAAAAAAFLldGQEAAAAQGoDAAAAAABAamMA
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