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)

pub 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()
}

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

pub fn read_vec2<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

pub fn read_col<T: std::str::FromStr>(n: usize) -> Vec<T> {
    (0..n).map(|_| read()).collect()
}

const R: u64 = 1000000007;

fn pow(a: u64, r: u64) -> u64 {
    if r == 0 {
        return 1;
    }
    let tmp = pow(a, r / 2);
    let mut ans = (tmp * tmp) % R;
    if r % 2 == 1 {
        ans = (ans * a) % R;
    }
    ans
}

fn main() {
    let xy: Vec<usize> = read_vec();
    let x = xy[0];
    let y = xy[1];
    if (x + y) % 3 != 0 || 2 * x < y || 2 * y < x {
        println!("0");
        return;
    }
    let n = (x + y) / 3;
    let r = 2 * n - x;
    let mut fact: Vec<u64> = vec![1; n + 1];
    for i in 1..n + 1 {
        fact[i] = (i as u64 * fact[i - 1]) % R;
    }
    let t1 = pow(fact[r], R - 2);
    let t2 = pow(fact[n - r], R - 2);
    let ans = (((fact[n] * t1) % R) * t2) % R;
    println!("{}", ans);
}