Problem:
Score : 400 points

Problem Statement

There is a knight - the chess piece - at the origin (0, 0) of a two-dimensional grid.

When the knight is at the square (i, j), it can be moved to either (i+1,j+2) or (i+2, j+1).

In how many ways can the knight reach the square (X, Y)?

Find the number of ways modulo 10^9 + 7.

Constraints

1 \leq X \leq 10^6

1 \leq Y \leq 10^6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X Y

Output

Print the number of ways for the knight to reach (X, Y) from (0, 0), modulo 10^9 + 7.

Sample Input 1

3 3

Sample Output 1

2

There are two ways: (0,0) \to (1,2) \to (3,3) and (0,0) \to (2,1) \to (3,3).

Sample Input 2

2 2

Sample Output 2

0

The knight cannot reach (2,2).

Sample Input 3

999999 999999

Sample Output 3

151840682

Print the number of ways modulo 10^9 + 7.

Solution in Rust (1.15.1) (judge verdict: Accepted)

#[allow(unused_imports)]
use std::cmp::{Ordering};

#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};

#[allow(unused_imports)]
use std::io::{stdin, stdout, BufWriter, Write};

#[allow(unused_imports)]
use std::iter::FromIterator;

#[allow(unused_macros)]
macro_rules! min {
    ($x: expr) => ($x);
    ($x: expr, $($z: expr),+) => {{
        std::cmp::min($x, min!($($z),*))
    }}
}

#[allow(unused_macros)]
macro_rules! max {
    ($x: expr) => ($x);
    ($x: expr, $($z: expr),+) => {{
        std::cmp::max($x, max!($($z),*))
    }}
}

#[allow(unused_macros)]
macro_rules! get { 
    ([$t: ty]) => { 
        { 
            let mut line = String::new(); 
            stdin().read_line(&mut line).unwrap(); 
            line.split_whitespace().map(|t|t.parse::<$t>().unwrap()).collect::<Vec<_>>()
        }
    };
    ([$t: ty];$n: expr) => {
        (0..$n).map(|_|get!([$t])).collect::<Vec<_>>()
    };
    ($t: ty) => {
        {
            let mut line = String::new();
            stdin().read_line(&mut line).unwrap();
            line.trim().parse::<$t>().unwrap()
        }
    };
    ($($t: ty),*) => {
        { 
            let mut line = String::new();
            stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            ($(iter.next().unwrap().parse::<$t>().unwrap(),)*)
        }
    };
    ($t: ty; $n: expr) => {
        (0..$n).map(|_|get!($t)).collect::<Vec<_>>()
    };
    ($($t: ty),*; $n: expr) => {
        (0..$n).map(|_|get!($($t),*)).collect::<Vec<_>>()
    };
}

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

const BIG_STACK_SIZE: bool = true;

#[allow(dead_code)]
fn main() {
    use std::thread;
    if BIG_STACK_SIZE {
        thread::Builder::new()
            .stack_size(32 * 1024 * 1024)
            .name("solve".into())
            .spawn(solve)
            .unwrap()
            .join()
            .unwrap();
    } else {
        solve();
    }
}

struct Comb {
    div: usize,
    g1: Vec<usize>,
    g2: Vec<usize>,
}
impl Comb {
#[allow(dead_code)]
    fn new(nmax: usize) -> Self {
        let mut g1 = vec![1; nmax + 1];
        let mut g2 = vec![1; nmax + 1];
        let mut inv = vec![0; nmax + 1];
        inv[1] = 1;
        let div = 1000000007;
        for i in 2..(nmax + 1) {
            g1[i] = g1[i - 1] * i % div;
            inv[i] = div - (inv[div % i] * (div / i)) % div;
            g2[i] = (g2[i - 1] * inv[i]) % div;
        }
        Comb {
            div: div,
            g1: g1,
            g2: g2,
        }
    }
#[allow(dead_code)]
    fn compute(&self, n: usize, k: usize) -> usize {
        (((self.g1[n] * self.g2[k]) % self.div) * self.g2[n - k]) % self.div
    }
#[allow(dead_code)]
    fn compute_dupc(&self, n: usize, k: usize) -> usize {
        self.compute(n + k - 1, n - 1)
    }
#[allow(dead_code)]
    fn compuute_perm(&self, n: usize, k: usize) -> usize {
        (self.g1[n] * self.g2[n - k]) % self.div
    }
}

fn solve() {
    let (x,y) = get!(usize, usize);
    if (x+y) % 3 > 0 {
        println!("0");
        return;
    }

    let m = (x+y)/3;
    if x < m || 2*m < x {
        println!("0");
        return;
    }
    let comb = Comb::new(m);
    println!("{}", comb.compute(m, x-m));
}