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: Time Limit Exceeded)

// Template from https://techracho.bpsinc.jp/jhonda/2019_08_05/78537

// input macro for competive-programming from https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        input_inner!{$s, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

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

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

#[allow(unused_macros)]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

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

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

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

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

fn main() {
    use std::io::Read;
    let mut s = String::new();
    std::io::stdin().read_to_string(&mut s).unwrap();

    println!("{}", solve(&s));
}

macro_rules! test {
    ($($exp_input:expr => $output:expr),* $(,)*) => {
        #[test]
        fn solve_test() {
            $(
                let start = std::time::Instant::now();
                let input = solve($exp_input);
                let end = start.elapsed();
                assert_eq!(input, $output, "{}.{:03}", end.as_secs(), end.subsec_millis());
                assert!(end.as_secs() <= 2, "expected_sec: {}sec, actual_sec: {}sec", 2, end.as_secs());
                assert!(end.as_secs() <= 1, "expected_sec: {}sec, actual_sec: {}sec", 1, end.as_secs());
                assert!(end.subsec_millis() <= 10, "expected_ms: {}ms, actual_ms: {}ms", 10, end.subsec_millis());
                assert!(end.subsec_millis() <= 2, "expected_ms: {}ms, actual_ms: {}ms", 2, end.subsec_millis());
            )*
        }
    };
}

test! {
// r#"3 3"# => r#"2"#,

// r#"2 2"# => r#"0"#,

r#"999999 999999"# => r#"151840682"#,
}

fn _dfs(s: (u64, u64), g: (u64, u64), ans: &mut usize) {
    if g.0 < s.0 || g.1 < s.1 {
        return;
    }

    if s.0 == g.0 && s.1 == g.1 {
        *ans += 1;
        return;
    }

   _dfs((s.0 + 1, s.1 + 2), g, ans);

   _dfs((s.0 + 2, s.1 + 1), g, ans);
}

fn dfs(x: u64, y: u64) -> usize {
    let mut ans = 0;
    _dfs((0, 0), (x, y), &mut ans);
    ans
}

fn solve(src: &str) -> String {
    let mut src_iter = src.split_whitespace();
    input! {
        source = src_iter,
        x: u64,
        y: u64,
    }

    (dfs(x, y) % 1_000_000_007).to_string()
}