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)

X, Y = map(int, input().split())
MD = pow(10, 9) + 7

def choose(n, a):
    x, y = 1, 1
    for i in range(a):
        x = x * (n - i) % MD
        y = y * (i + 1) % MD
    return x * pow(y, MD - 2, MD) % MD

a = (2*Y-X)//3
b = (Y-2*X)//-3
if a < 0 or b < 0 or (X+Y) % 3 != 0:
    print(0)
    exit()
print(choose(a+b, min(a,b)))