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(non_snake_case, unused)]
use std::cmp::*;
use std::collections::*;

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, [ $t:tt ]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

struct Comb {
    fac: Vec<u64>,
    finv: Vec<u64>,
    inv: Vec<u64>,
    m: u64,
}

impl Comb {
    fn new(n: usize, m: u64) -> Comb {
        let mut fac = vec![0u64; n];
        let mut finv = vec![0u64; n];
        let mut inv = vec![0u64; n];

        fac[0] = 1;
        fac[1] = 1;
        finv[0] = 1;
        finv[1] = 1;
        inv[1] = 1;

        for i in 2..n {
            fac[i] = fac[(i - 1) as usize] * i as u64 % m;
            inv[i] = m - inv[(m % i as u64) as usize] * (m / i as u64) % m;
            finv[i] = finv[(i - 1) as usize] * inv[i] % m;
        }
        Comb {
            fac: fac,
            finv: finv,
            inv: inv,
            m: m,
        }
    }
    fn calc(&self, n: usize, k: usize) -> u64 {
        if n < k {
            return 0;
        }

        return self.fac[n] * (self.finv[k] * self.finv[n - k] % self.m) % self.m;
    }
}
//

const MOD: u64 = 1_000_000_000 + 7;
fn main() {
    input! {
        x: i64,
        y: i64,
    }
    let mut cnt = 0;
    if (x+y) % 3 != 0 {
        return println!("0")
    }
    let n = (2 * y - x)/ 3;
    let m = y - 2 * (2 * y - x) / 3;
    
    if min(n, m) < 0 {
        return println!("0")
    }

    let cmb = Comb::new((n + m+2) as usize, MOD);    
    println!("{}", cmb.calc((n + m) as usize, n as usize));
}