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 cmb(n, r, p):
    if r<0 or n<r:
        return 0
    r=min(r, n-r)
    return fact[n]*factinv[r]*factinv[n-r]%p

mod=10**9+7
MAXN=2*10**6+10
fact=[1, 1]
factinv=[1, 1]
inv=[0, 1]

for i in range(2, MAXN+1):
    fact.append((fact[-1]*i)%mod)
    inv.append(-inv[mod%i]*(mod//i)%mod)
    factinv.append((factinv[-1]*inv[-1])%mod)

x,y=map(int, input().split())
res=0
if (x+y)%3==0:
    m=(2*x-y)//3
    n=(2*y-x)//3
    res=cmb(m+n,m,mod)
print(res)