extern crate core;

use std::fmt;
use std::i32::{MAX};
use std::cmp::{Ordering, min, max };
use std::ops::{Add, Sub, Mul, Div, Neg, Index, IndexMut, SubAssign, Range};
use std::collections::{BTreeMap, VecDeque, BinaryHeap, BTreeSet, HashMap};
use std::fmt::{Display, Formatter, Error};

fn show<T: Display>(vec: &Vec<T>) {
    if vec.is_empty() {
        println!("[]");
    }else {
        print!("[{}", vec[0]);
        for i in 1 .. vec.len() {
            print!(", {}", vec[i]);
        }
        println!("]");
    }
}
fn show2<T: Display>(vec: &Vec<Vec<T>>) {
    if vec.is_empty() {
        println!("[]");
    }else {
        for l in vec {
            show(l);
        }
    }
}
macro_rules! read_lines{
    ($count: expr; $delimiter: expr; $ty: ty) => {{
        let line_count = $count;
        let mut vec: Vec<Vec<$ty>> = Vec::with_capacity(line_count);
        for _ in 0 .. line_count {
            vec.push(read_line!($delimiter; $ty));
        }
        vec
    }};
    ($count: expr; $ty: ty) => {{
        let line_count = $count;
        let mut vec: Vec<$ty> = Vec::with_capacity(line_count);
        for _ in 0 .. line_count {
            vec.push(read_value!());
        }
        vec
    }}
}
macro_rules! read_line{
    () => {{
        let mut line = String::new();
        std::io::stdin().read_line(&mut line).ok();
        line
    }};
    (delimiter: ' ') => {
        read_line!().split_whitespace().map(|x|x.to_string()).collect::<Vec<_>>()
    };
    (delimiter: $p:expr) => {
        read_line!().split($p).map(|x|x.to_string()).collect::<Vec<_>>()
    };
    (' ') => {
        read_line!(delimiter: ' ')
    };
    ($delimiter:expr) => {
        read_line!(delimiter: $delimiter)
    };
    (' '; $ty:ty) => {
        read_line!().split_whitespace().map(|x|x.parse::<$ty>().ok().unwrap()).collect::<Vec<$ty>>()
    };
    ($delimiter:expr; $ty:ty) => {
        read_line!($delimiter).into_iter().map(|x|x.parse::<$ty>().ok().unwrap()).collect::<Vec<$ty>>()
    };
}
macro_rules! read_value{
    () => {
        read_line!().trim().parse().ok().unwrap()
    }
}
macro_rules! let_all {
    ($($n:ident:$t:ty),*) => {
        let line = read_line!(delimiter: ' ');
        let mut iter = line.iter();
        $(let $n:$t = iter.next().unwrap().parse().ok().unwrap();)*
    };
}

macro_rules! let_mut_all {
    ($($n:ident:$t:ty),*) => {
        let line = read_line!(delimiter: ' ');
        let mut iter = line.iter();
        $(let mut $n:$t = iter.next().unwrap().parse().ok().unwrap();)*
    };
}
fn main(){
    const MOD: i64 = 1000000007i64;
    let_all!(n: usize, m: usize, k: usize);
    let mut factorial = vec![1i64; n + m + k * 2+ 1];
    let mut inv = vec![1i64; n + m + k * 2 + 1];
    let mut inv_factorial = vec![1i64; n + m + k * 2 + 1];
    for i in 2.. factorial.len() {
        factorial[i] = i as i64 * factorial[i - 1] as i64 % MOD;
        inv[i] = (MOD - MOD / i as i64) * inv[(MOD % i as i64) as usize] % MOD;
        inv_factorial[i] = inv[i] * inv_factorial[i - 1] % MOD;
    }
    let factorial = factorial; let inv_factorial = inv_factorial;
    let mut result = 0i64;
    //show(&inv_factorial);
    for i in 0 .. k + 1 {
        let j = k - i;
        let for_vertical = if i == 0 {1i64} else {(factorial[n + i * 2] * inv_factorial[i] % MOD * inv_factorial[n + i] % MOD - factorial[n + i * 2] * inv_factorial[i - 1] % MOD * inv_factorial[n + i + 1] % MOD) % MOD};
        let for_horizontal = if j == 0 {1i64} else {(factorial[m + j * 2] * inv_factorial[j] % MOD * inv_factorial[m + j] % MOD - factorial[m + j * 2] * inv_factorial[j - 1] % MOD * inv_factorial[m + j + 1] % MOD) % MOD};
        result += for_vertical * for_horizontal % MOD * factorial[n + m + k * 2] % MOD * inv_factorial[n + i * 2] % MOD * inv_factorial[m + j * 2] % MOD;
        result %= MOD;
    }
    println!("{}", (result + MOD) % MOD);
}


Measured memory_bytes: 7656