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: Wrong Answer)

use std::io::*;
use std::str::FromStr;

pub fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn main() {
    let a = read::<i64>();
    let b = read::<i64>();
    let m_min = std::cmp::min(a, b);
    let m_max = std::cmp::max(a, b);

    let mut base = m_min - (m_max - m_min);

    if (base % 3 != 0) || (m_max-base) != (m_min-base) * 2 {
        println!("0");
        return;
    }
    let hi = (m_max-base) / 2;
    base = (base*2) / 3;
    let top_n = base+hi;
    
    let mut top:f64 = 1.0;

    println!("{} {} {}",base+top_n, base, top_n);
    for i in 0..(base+top_n) as usize {
        top *= (i+1) as f64;
        top = top % 100_000_000_7.0;
    }
    let mut under1:f64 = 1.0;
    for i in 0..top_n as usize {
        under1 *= (i+1) as f64;
        under1 = under1 % 100_000_000_7.0;
    }
    let mut under2:f64 = 1.0;
    for i in 0..base as usize {
        under2 *= (i+1) as f64;
        under2 = under2 % 100_000_000_7.0;
    }
    println!("{}", (top/(under1*under2)) % (100_000_000_7.0))
}