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: Accepted)

P = 10**9 + 7
X, Y = map(int, input().split())

def factorial(n):
    res = 1
    for i in range(2, n+1):
        res *= i
        res %= P
    return res

if (2*X-Y)%3 == 0 and (-X+2*Y)%3 == 0 and 2*X-Y >= 0 and -X+2*Y >= 0:
    a = (-X+2*Y)//3
    b = (2*X-Y)//3
    print((factorial(a+b)*pow(factorial(a), P-2, P)*pow(factorial(b), P-2, P))%P)
else:
    print(0)