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 (3.8.2) (judge verdict: Accepted)

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

def nCk(n,k,p):
    fact    = [1,1] + [0]*(n-1)
    inv     = [0,1] + [0]*(n-1)
    factinv = [1,1] + [0]*(n-1)
    
    for i in range(2, n+1):
        fact[i] = i * fact[i-1] % p
        inv[i] = - inv[p % i] * (p // i) % p
        factinv[i] = factinv[i-1] * inv[i] % p
    
    return fact[n] * factinv[k] * factinv[n-k] % p

ans = 0
if (X + Y) % 3 == 0 and X <= 2*Y and Y <= 2*X:
    a = (2*Y - X) // 3
    b = (2*X - Y) // 3
    ans = nCk(a+b, a, mod)
print(ans)