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)

// https://atcoder.jp/contests/abc145/tasks/abc145_d
//
#![allow(unused_imports)]
use std::io::*;
use std::fmt::*;
use std::str::*;
use std::cmp::*;
use std::collections::*;

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($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, [ next / $t:tt ]) => {
        {
            let len = read_value!($iter, usize);
            (0..len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
        }
    };

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

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

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

#[allow(unused_macros)]
macro_rules! dvec {
    ($t:expr ; $len:expr) => {
        vec![$t; $len]
    };

    ($t:expr ; $len:expr, $($rest:expr),*) => {
        vec![dvec!($t; $($rest),*); $len]
    };
}

#[allow(unused_macros)]
macro_rules! ifv {
    ($t:expr, $a:expr, $b: expr) => {
        if $t { $a } else { $b }
    }
}

#[allow(unused_macros)]
macro_rules! fill {
    ($t:expr, $v:expr) => {
        for i in 0..$t.len() {
            $t[i] = $v;
        }
    };
}

#[allow(unused_macros)]
macro_rules! join {
    ($t:expr, $glue:expr) => {
        $t.into_iter().map(|w| w.to_string()).collect::<Vec<_>>().join($glue)
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        println!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
    }
}

const MOD: u64 = 1000000007;

struct Combination {
    fact: Vec<u64>,
    invfact: Vec<u64>,
}

impl Combination {
    fn inv(a: u64) -> u64 {
        Combination::pow(a, MOD - 2)
    }

    fn pow(a: u64, p: u64) -> u64 {
        let mut p = p;
        let mut aa = a;
        let mut ret = 1;
        while p >= 1 {
            if p & 1 == 1 {
                ret *= aa;
                ret %= MOD;
            }
            p >>= 1;
            aa = aa * aa % MOD;
        }
        ret
    }

    fn new(upto: usize) -> Self {
        let mut fact = vec![0; upto];
        let mut invfact = vec![0; upto];

        fact[0] = 1;
        for i in 1..upto {
            fact[i] = fact[i - 1] * (i as u64) % MOD;
        }

        invfact[upto - 1] = Combination::inv(fact[upto - 1]);
        invfact[0] = 1;
        for i in (1..upto - 1).rev() {
            invfact[i] = invfact[i + 1] * ((i + 1) as u64) % MOD;
        }

        Combination {
            fact: fact,
            invfact: invfact,
        }
    }

    fn comb(&self, n: usize, r: usize) -> u64 {
        if r < 0 || r > n {
            return 0;
        }
        self.fact[n] * self.invfact[r] % MOD * self.invfact[n - r] % MOD
    }
}

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

    let mut c = Combination::new(1000010);

    let mut total = 0;
    for t in 0..x+1 {
        if t <= x && t*2 <= y {
            let lx = x-t;
            let ly = y-2*t;
            if lx == ly*2 {
                total += c.comb(t+ly, t);
                total %= MOD;
            }
        }
    }

    println!("{}", total);
}