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)

x, y = gets.split.map &:to_i

remain = 0
diff = (x-y).abs
MOD = 10 ** 9 + 7

if x >= y then
	remain = y - (x - y)
else
	remain = x - (y - x)
end

if remain % 3 == 0 then
	ss = remain / 3
	ll = ss + (x-y).abs
	
	sum = 1
	
	(ss + 1 .. (ss+ll)).each{ |i|
		sum = sum * i % MOD
	}

	arr = (MOD-2).to_s(2).split("").reverse

	a = 1

	(1..ll).each{ |i|
		a = a * i % MOD
	}

	div = 1

	arr.each{ |i|
		if i == "1" then
			div = div * a % MOD
		end
		a = a * a % MOD
	}

	sum = sum * div % MOD

	puts sum
else
	puts 0
end