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 (3.4.3) (judge verdict: Wrong Answer)

X, Y = map(int, input().split())
mod = 10**9+7
b = (2*Y-X)//3
a = Y - 2*b
print(a, b)
max_num = a + b + 5
facts = [1 for i in range(max_num)]
invs = [1 for i in range(max_num)]
 
def inv(x):
    return pow(x,mod-2,mod)
 
for i in range(1,max_num):
    facts[i] = facts[i-1]*i%mod
    invs[i] = inv(facts[i])
 
def nCk(n,k):
    try:
        return facts[n]*invs[k] * invs[n-k] % mod
    except IndexError:
        print(n, k, len(facts), len(invs))
if (X+Y)%3 == 0 and a>=0 and b >=0:
    print(nCk(a+b, a))
else:
    print(0)