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)

use std::str::FromStr;
use std::fmt::Debug;
use std::cmp;

#[allow(dead_code)]
fn read_as_vec<T>() -> Vec<T>
where T: FromStr, <T as FromStr>::Err : Debug{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().map(|c| T::from_str(c).unwrap()).collect()

}

struct CombMod{
    fac: Vec<u64>,
    inv: Vec<u64>,
    finv: Vec<u64>,
    mmod: u64,
}

impl CombMod{
    pub fn new(max: u64, m: u64) -> CombMod{
        let max: usize = max as usize;
        let mut fac: Vec<u64> = vec![0;max+1];
        let mut finv: Vec<u64> = vec![0;max+1];
        let mut inv: Vec<u64> = vec![0;max+1];

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

        for i in 2..max+1{
            fac[i] = fac[i-1] * i as u64 % m;
            inv[i] = m - inv[m as usize %i] * (m/(i as u64)) % m;
            finv[i] = finv[i-1] * inv[i] % m;
        }

        CombMod{
            fac: fac,
            finv: finv,
            inv: inv,
            mmod: m,
        }
    }

    fn get(&self, n: u64, m: u64) -> u64{
        assert!(n >= m && n != 0 && m != 0);
        self.fac[n as usize] * self.finv[m as usize] % self.mmod
            * self.finv[(n-m) as usize] % self.mmod
    }
}


fn main(){
    let line = read_as_vec::<u64>();
    let (x, y) = (line[0], line[1]);

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


    let mut mov: (u64, u64) = (0, 0);
    // v = the number of move (2, 1)
    for v in 0..x+1{
        if (x - v)%2 != 0{
            continue;
        }

        let h = (x - v)/2;

        if y == (2*v + h) && x == (v + 2*h){
            mov = (h, v);
            break;
        }
    }

    if mov == (0, 0){
        println!("0");
        return;
    }
    let comb = CombMod::new(mov.0 + mov.1, 1_000_000_007);
    println!("{}", comb.get(mov.0 + mov.1, cmp::max(mov.0, mov.1)));
}