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: Runtime Error)

def inv(a,p):
    if a==1:
        return 1
    else:
        return p-(inv(p%a,p)*(p//a))%p
x,y=map(int,input().split())
if (x+y)%3!=0:
    print("0")
    exit()
n=(x+y)//3
r=(2*x-y)//3
p=10**9+7
def fact(n,p):
    a=[[] for _ in range(n+1)]
    a[0]=1
    for i in range(n):
        a[i+1]=(a[i]*(i+1))%p
    return(a)
f=fact(n,p)
c=f[-1]
d=f[r]
e=f[n-r]
dd=inv(d,p)
ee=inv(e,p)
ans=(c*dd*ee)%p
print(ans)