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: Accepted)

mod = 10**9 + 7

fact_range = 10**6
facts = [1] * (fact_range + 1)
for i in range(0, fact_range):
    facts[i+1] = facts[i] * (i + 1) % mod

ifacts = [1] * (fact_range + 1)
ifacts[fact_range] = pow(facts[fact_range], mod - 2, mod)
for i in range(fact_range, 0, -1):
    ifacts[i-1] = ifacts[i] * i % mod

def comb(n, k):
    if k < 0 or n < k:
        return 0
    else:
        return facts[n] * ifacts[n-k] % mod * ifacts[k] % mod

x, y = map(int, input().split())
if (x + y) % 3:
    print(0)
else:
    n = (x + y) // 3
    k = x - n
    print(comb(n, k))