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)

use std::cmp::*;

fn main() {
    let v = read_vec::<usize>();
    let x = v[0];
    let y = v[1];
    let div = 1000000007;
    if (x + y) % 3 != 0 || max(x, y) / min(x, y) > 2 {
        println!("0");
        return;
    }

    let nx = (x + y) / 3;
    let ny = (nx + y - x) / 2; // ((x - y)*(-1)+nx) / 2
    //println!("{}, {}", nx, ny);

    let mut dp = vec![vec![0u64; nx + 1]; nx + 1];
    dp[0][0] = 1;
    for i in 0..nx {
        for j in 0..i + 1 {
            dp[i + 1][j] += dp[i][j];
            dp[i + 1][j] %= div;
            dp[i + 1][j + 1] += dp[i][j];
            dp[i + 1][j + 1] %= div;
        }
    }
    //println!("{:?}", dp);
    println!("{}", dp[nx][ny]);
}

#[allow(dead_code)]
fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}
#[allow(dead_code)]
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}
#[allow(dead_code)]
fn read_vec2<T: std::str::FromStr>(n: u32) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}
#[allow(dead_code)]
fn yn(result: bool) {
    if result {
        println!("Yes");
    } else {
        println!("No");
    }
}