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)

def xgcd a, b
	x, y, u, v = 1, 0, 0, 1
	until b == 0
		q, a, b = a/b, b, a%b
		x, y, u, v = u, v, x-q*u, y-q*v
	end
	return a, x, y
end
def imod a, m
	d, x, y = xgcd a, m
	return nil unless d == 1
	return 0<x ? x : x+m
end

X, Y = gets.split.map(&:to_i)
MOD = 1000000007
(p 0; exit) unless (X+Y)%3 == 0
L, R = [Y-(X+Y)/3, 2*(X+Y)/3-Y].minmax
(p 0; exit) if L < 0
p((R+1..L+R).inject(1){|s,n| s*n%MOD } * imod((1..L).inject(1){|s,d| s*d%MOD },MOD) % MOD)