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)

#![allow(non_snake_case)]
#![allow(dead_code)]
#![allow(unused_macros)]
#![allow(unused_imports)]

use std::cmp::*;
use std::collections::*;

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)*}
    };
}

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)*}
    }
}

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<_>>()
    };

    ($iter:expr, chars) => {
        read_value!($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")
    };
}

macro_rules! chmax {
    ($x:expr, $e:expr) => {
        if $x < $e {
            $x = $e;
        }
    };
}
macro_rules! chmin {
    ($x:expr, $e:expr) => {
        if $x > $e {
            $x = $e;
        }
    };
}

use std::ops::*;

const MOD: usize = 1000000007;
#[derive(Copy, Clone)]
struct ModInt {
    n: usize,
}

impl ModInt {
    fn from_usize(n: usize) -> ModInt {
        ModInt { n: n % MOD }
    }
    fn pow(self, power: usize) -> ModInt {
        if power == 0 {
            return ModInt::from_usize(1);
        }
        if power % 2 == 0 {
            let t = self.pow(power/2);
            return t * t;
        }
        self * self.pow(power-1)
    }
    fn inv(self) -> ModInt {
        self.pow(MOD - 2)
    }
}

impl Add for ModInt {
    type Output = ModInt;

    fn add(self, rhs: ModInt) -> ModInt {
        let mut tmp = self;
        tmp.n += rhs.n;
        if tmp.n >= MOD {
            tmp.n -= MOD;
        }
        tmp
    }
}

impl AddAssign for ModInt {
    fn add_assign(&mut self, rhs: ModInt) {
        *self = *self + rhs;
    }
}

impl Sub for ModInt {
    type Output = ModInt;

    fn sub(self, rhs: ModInt) -> ModInt {
        let mut tmp = self;
        if tmp.n < rhs.n {
            tmp.n += MOD;
        }
        tmp.n -= rhs.n;
        tmp
    }
}

impl SubAssign for ModInt {
    fn sub_assign(&mut self, rhs: ModInt) {
        *self = *self - rhs;
    }
}

impl Mul for ModInt {
    type Output = ModInt;

    fn mul(self, rhs: ModInt) -> ModInt {
        let mut tmp = self;
        tmp.n *= rhs.n;
        tmp.n %= MOD;
        tmp
    }
}

impl MulAssign for ModInt {
    fn mul_assign(&mut self, rhs: ModInt) {
        *self = *self * rhs;
    }
}

impl Div for ModInt {
    type Output = ModInt;

    fn div(self, rhs: ModInt) -> ModInt {
        let mut tmp = self;
        tmp.n *= rhs.inv().n;
        tmp.n %= MOD;
        tmp
    }
}

impl DivAssign for ModInt {
    fn div_assign(&mut self, rhs: ModInt) {
        *self = *self / rhs;
    }
}

fn fact(n: ModInt) -> ModInt {
    let mut r = ModInt::from_usize(1);
    for i in 1..(n.n+1) {
        r *= ModInt::from_usize(i);
    }
    r
}

fn comb(n: ModInt, k: ModInt) -> ModInt {
    fact(n) / (fact(k) * fact(n - k))
}

const INF: i64 = 1 << 60;

fn main() {
    input!{
        X: usize,
        Y: usize,
    }
    if (X + Y) % 3 != 0 {
        println!("0");
        return;
    }
    let N = (X + Y) / 3;
    let K = max(X, Y) - N;
    let N = ModInt::from_usize(N);
    let K = ModInt::from_usize(K);
    println!("{}", comb(N, K).n);
}