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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

[x,y]=list(map(int,input().split()))
if ((x%3)+(y%3))%3!=0:
	print(0)
else:
	dansu=int((x+y)/3)
	r=y-dansu
	mod=1000000007
	d=1
	rr=1
	nr=1
	for i in range(1,dansu+1):
		d=d*(i%mod)
	for i in range(1,r+1):
		rr=rr*(i%mod)
	for i in range(1,dansu-r+1):
		nr=nr*(i%mod)
	
	kotae=int((d%mod)*((rr**(mod-2))%mod)*((nr**(mod-2))%mod))
	kotae=int(kotae%(10**9+7))
	
	print(kotae)