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: Wrong Answer)

mod = 10**9+7

def fact(n):
    ans = 1
    for i in range(2,n+1):
        ans *= i
        ans %= mod
    return ans
    
X,Y = list(map(int,input().split()))

# a+2b = X
# 2a+b = Y を解く
# -> a = (2Y-X)/3, b = (2X-Y)/3
# (i+1,j+2) の移動が a 回
# (i+2,j+1) の移動が b 回

a = (2*Y-X)/3
b = (2*X-Y)/3 

if not a.is_integer() or not b.is_integer():
    print(0)
    exit(0)

# a回とb回の移動の組み合わせは (a+b)!/a!b!
print(fact(int(a+b)) * pow(fact(int(a)),mod-2,mod) * pow(fact(int(b)),mod-2,mod) % mod)