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)

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|s| s.parse().ok().unwrap())
        .collect()
}

fn mod_pow(a: i64, n: i64, p: i64) -> i64 {
    match n {
        0 => 1,
        n if n % 2 == 0 => {
            let x = mod_pow(a, n/2, p);
            x * x % p
        },
        _ => {
            let x = mod_pow(a, n/2, p);
            a * (x*x % p) % p
        }
    } 
}

fn mod_combination(n: i64, r: i64, p: i64) -> i64 {
    let mut x = 1;
    for i in 0..r {
        x = x *(n - i) % p;
    }
    let mut y = 1;
    for i in 1..r+1 {
        y = y * i % p;
    }
    x * mod_pow(y, p - 2, p) % p
}

const MODULO: i64 = 1_000_000_007;

fn main() {
    let input = read_vec::<i64>();
    let (x, y) = (input[0], input[1]);

    if (x + y) % 3 != 0 {
        println!("0");
        return;
    }

    let n = (2*x - y) / 3;
    let m = (2*y - x) / 3;

    if (2*x - y) % 3 != 0 || (2*y - x) % 3 != 0 {
        println!("0");
        return;
    }

    if n < 0 || m < 0 {
        println!("0");
        return;
    }
    
    let ans = mod_combination(n+m, n, MODULO);
    println!("{}", ans);
}