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: Wrong Answer)

x, y = map(int, input().split())
mod = 10 ** 9 + 7
if (x == 1 and y == 2) or (x == 2 and y == 1):
    print(1)
    quit()
if (x % 3 == 0 and y % 3 != 0) or (x % 3 != 0 and y % 3 == 0):
    print(0)
    quit()
ans = 1
ans = 2 ** (x//3)
# for i in range(1, x // 3+1):
#     ans *= 2
# for j in range(1, y // 3+1):
#     ans *= 2
print(ans % mod)