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 (7.3.0) (judge verdict: Wrong Answer)

X, Y = map(int, input().split())

mod = 10**9+7
def factorial(N):
    if N==1 or N==1:
        return 1
    else:
        ans = N
        for i in range(1, N):
            ans*=N-i
            ans%=mod
        return ans

if 2*Y-X>=0 and (2*Y-X)%3==0 and 2*X-Y>=0 and (2*X-Y)%3==0:
    s = (2*X-Y)//3
    t = (2*Y-X)//3
    #print(s, t)
    a = factorial(s+t)
    b = pow(factorial(s), mod-2, mod)
    c = pow(factorial(t), mod-2, mod)
    #print(a, b, c)
    print((a*b*c)%mod)
else:
    print(0)