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)

#[allow(unused_macros)]
macro_rules! input_byline {
    ($($r:tt)* ) => {
        let stdin = std::io::stdin();
        let mut q = std::collections::VecDeque::new();
        let mut next = || {
            if q.is_empty() {
                let mut s = String::new();
                stdin.read_line(&mut s);
                for v in s.split_whitespace() {
                    q.push_back(v.to_string());
                }
            }
            q.pop_front().unwrap()
        };
        input_inner!{next, $($r)*}
    };

}

#[allow(unused_macros)]
macro_rules! input {
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

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

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

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

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

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

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

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

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

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

trait Printable {
    fn p(&self);
}

impl<T: std::fmt::Display> Printable for T {
    fn p(&self) {
        println!("{}", self);
    }
}

impl<T: std::fmt::Display> Printable for [T] {
    fn p(&self) {
        for i in 0..self.len() {
            if i != 0 {
                print!(" ");
            }
            print!("{}", self[i]);
        }
        println!("");
    }
}

#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{BinaryHeap, HashMap};

#[allow(dead_code)]
type Graph = Vec<Vec<usize>>;

struct Combination {
    modp: usize,
    mfact: Vec<usize>,
    rfact: Vec<usize>,
}

impl Combination {
    fn new(size: usize, modp: usize) -> Self {
        let mut rfact = vec![0; size + 1];
        let mut mfact = vec![0; size + 1];
        mfact[0] = 1;
        for i in 1..mfact.len() {
            mfact[i] = (mfact[i - 1] * i) % modp;
        }
        rfact[size] = Self::inv(mfact[size], modp);
        for i in (0..size).rev() {
            rfact[i] = rfact[i + 1] * (i + 1) % modp;
        }

        Combination {
            modp: modp,
            mfact: mfact,
            rfact: rfact,
        }
    }

    fn pow(mut x: usize, mut n: usize, modp: usize) -> usize {
        let mut ret = 1;
        while n > 0 {
            if n & 1 > 0 {
                ret *= x;
                ret %= modp;
            }
            x *= x;
            x %= modp;
            n >>= 1;
        }
        ret
    }

    fn inv(x: usize, modp: usize) -> usize {
        Self::pow(x, modp - 2, modp)
    }

    fn C(&self, p: usize, q: usize) -> usize {
        if p < q {
            return 0;
        }
        (((self.mfact[p] * self.rfact[q]) % self.modp) * self.rfact[p - q]) % self.modp
    }
}

fn main() {
    input! {
        x: usize,
        y: usize,
    }

    let mut cx = 0;
    let mut cy = 0;
    let mut ok = false;

    for i in 0..x + 1 {
        let xx = i;
        let yy = i * 2;
        if x >= xx && y >= yy && (y - yy) * 2 == (x - xx) {
            cx = i;
            cy = y - yy;
            ok = true;
            break;
        }
    }
    if !ok {
        println!("0");
        return;
    }

    let comb = Combination::new(1111111, 1000000007);
    println!("{}", comb.C(cx + cy, cx));
}