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: Runtime Error)

[x,y]=list(map(int,input().split()))
if ((x%3)+(y%3))%3!=0:
	print(0)
else:
	n=int((x+y)/3)
	r=y-n
	if r<0 or r>n:
		print(0)
	else:
		if r>n-r:
			r=n-r
		mod=1000000007
		kaijo=[1]
		for i in range(1,n+1):
			kaijo.append(kaijo[-1]*i%mod) #これで、kaijo[i]=i!となる。
		gyakugen=[pow(kaijo[n-r],mod-2,mod)]
		for i in reversed(range(1,n-r)):
			gyakugen.append(gyakugen[-1]*i) #これで、gyakugen[i]=n-r-iの逆元となる
		kotae=kaijo[n]*gyakugen[0]*gyakugen[n-2*r]%mod

		print(kotae)