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 Ruby (2.3.3) (judge verdict: Accepted)

# 二項係数nCk mod p
# 前処理
MOD = 10**9 + 7
@fac, @finv, @inv = [], [], []
def comInit
    @fac[0] = @fac[1] = 1
    @finv[0] = @finv[1] = 1
    @inv[1] = 1
    (2...(10 ** 6)).each {|i|
        @fac[i] = @fac[i-1] * i % MOD
        @inv[i] = MOD - @inv[MOD % i] * (MOD / i) % MOD
        @finv[i] = @finv[i-1] * @inv[i] % MOD
    }
end

def com n, k
    if (n < k)
        return 0
    end
    if (n < 0 || k < 0)
        return 0
    end
    return @fac[n] * (@finv[k] * @finv[n - k] % MOD) % MOD;
end

X, Y = gets.split(' ').map(&:to_i)

def func x, y
    a = (2 * x - y) / 3
    b = (2 * y - x) / 3
    return a, b
end

if (X + Y) % 3 != 0
    puts 0
    exit
end

A, B = func X, Y

comInit

puts (com A + B, B)