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 PyPy3 (2.4.0) (judge verdict: Accepted)

def mod_inv(a, m):
    return pow(a,m-2,m)


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

if (X + Y) % 3:
    print(0)
    exit()

n = (X + Y) // 3
nx, ny = X - n, Y - n

if nx < 0 or ny < 0:
    print(0)
    exit()

ans = 1
for i in range(1, nx + ny + 1):
    ans = ans * i % MOD
for i in range(1, nx + 1):
    ans = ans * mod_inv(i, MOD) % MOD
for i in range(1, ny + 1):
    ans = ans * mod_inv(i, MOD) % MOD

print(ans)