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 main() {
    let xy = read_vec::<u64>();
    let x = xy[0];
    let y = xy[1];

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

    println!("{}", comb(a + b, a));
}

fn comb(a: u64, b: u64) -> u64 {
    const MOD: u64 = 1000000007;
    let b = {
        let tmp = a - b;
        if tmp < b { tmp } else { b }
    };

    let mut ch = 1;
    for i in 0..b {
        ch *= a - i;
        ch %= MOD;
    }

    let mut mo = 1;
    let mut x = b;
    while x > 0 {
        mo *= x;
        mo %= MOD;
        x -= 1;
    }

    ch * exp(mo, MOD-2) % MOD
}

fn exp(a: u64, n: u64) -> u64 {
    if n == 0 {
        return 1
    }

    const MOD: u64 = 1000000007;
    if n % 2 == 1 {
        a * exp(a, n-1) % MOD
    } else {
        let tmp = exp(a, n / 2);
        tmp * tmp % MOD
    }
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().split_whitespace().map(|e| e.parse().ok().unwrap()).collect()
}