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 (1.42.0) (judge verdict: Accepted)

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

#[allow(dead_code)]
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 pow_mod(base: i64, power: i64, modulo: i64) -> i64 {
    let mut base = base;
    let mut power = power;
    let mut ans = 1;
    while power > 0 {
        if power & 1 == 1 {
            ans = ans * base % modulo;
        }
        power >>= 1;
        base = base * base % modulo;
    }
    ans
}

#[allow(dead_code)]
fn inv_mod(a: i64, modulo: i64) -> i64 {
    pow_mod(a, modulo - 2, modulo)
}

const MOD: i64 = 1e+9 as i64 + 7;
const FACT_MAX: usize = 1000010;
static mut FACTORIAL: [i64; FACT_MAX + 1] = [0; FACT_MAX + 1];
static mut RFACTORIAL: [i64; FACT_MAX + 1] = [0; FACT_MAX + 1];
fn init_fact() {
    unsafe {
        if FACTORIAL[0] == 0 {
            FACTORIAL[0] = 1;
            for i in 1..FACT_MAX + 1 {
                FACTORIAL[i] = (FACTORIAL[i - 1] * i as i64) % MOD;
            }
            RFACTORIAL[FACT_MAX] = inv_mod(FACTORIAL[FACT_MAX], MOD);
            for i in (0..FACT_MAX).rev() {
                RFACTORIAL[i] = RFACTORIAL[i + 1] * (i as i64 + 1) % MOD;
            }
        }
    }
}
#[allow(dead_code)]
fn fact(n: usize) -> i64 {
    init_fact();
    unsafe { FACTORIAL[n] }
}
#[allow(dead_code, unused_comparisons)]
fn combi(n: usize, m: usize) -> i64 {
    if n < m || m < 0 {
        return 0;
    }
    init_fact();
    unsafe { FACTORIAL[n] * RFACTORIAL[m] % MOD * RFACTORIAL[n - m] % MOD }
}

fn main() {
    init_fact();
    let x = read::<usize>();
    let y = read::<usize>();
    let mut ans = 0;
    for dx in 0..x + 1 {
        let rx = x - dx;
        if 2 * dx > y {
            continue;
        }
        let dy = y - 2 * dx;
        if dy * 2 != rx {
            continue;
        }
        ans = (ans + combi(dx + dy, dy)) % MOD;
    }
    println!("{}", ans);
}