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)

X,Y = map(int,input().split())
if (X + Y) % 3 != 0:
    print(0)
    exit()
n = (-X+2*Y)//3
m = (2*X-Y)//3
if n < 0 or m < 0:
    print(0)
    exit()

mod = 10**9+7
mod_inv = [0, 1] + [0] * (max(n,m)+3)
for i in range(2, max(n,m)+5):
    mod_inv[i] = - mod_inv[mod % i] * (mod // i) % mod
def comod(n, r, mod):
    ans = 1
    for i in range(r):
        ans *= (n-i) % mod
        ans *= mod_inv[i+1]
        ans %= mod
    return ans
ans = comod(n+m,n,mod)
print(ans)