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::io::{stdin, Read};
use std::str::FromStr;

// https://qiita.com/tubo28/items/e6076e9040da57368845
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")
}

#[allow(dead_code)]
fn main() {
    let x = read::<i64>();
    let y = read::<i64>();

    let mut cx = 0;
    let mut cy = 0;

    for i in 0..x + 1 {
        let rx = x - i;
        let ry = y - 2 * i;
        if rx % 2 == 0 && ry == rx / 2 {
            cy = i;
            cx = rx / 2;

            println!("{}", comb_m((cx + cy) as usize, (cy) as usize, 1000000007));
            return;
        }
    }
    println!("0");

    // https://abc034.contest.atcoder.jp/submissions/7354299
    fn pow_m(n: usize, mut p: usize, d: usize) -> usize {
        let mut r = n;
        let mut ret = 1;
        while p > 0 {
            if p % 2 == 0 {
                r = r * r % d;
                p /= 2;
            } else {
                ret = ret * r % d;
                p -= 1;
            }
        }
        ret
    }

    fn inv_m(n: usize, d: usize) -> usize {
        pow_m(n, d - 2, d)
    }

    fn comb_m(n: usize, r: usize, d: usize) -> usize {
        (n - r + 1..n + 1).fold(1, |ac, x| ac * x % d)
            * inv_m((1..r + 1).fold(1, |ac, x| ac * x % d), d)
            % d
    }
}