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)

x, y = map(int,input().split())
M = 1000000007

if (x + y) % 3 != 0:
    print(0)
    exit()

if max(x,y) / min(x,y) > 2:
    print(0)
    exit()

n = (x + y) // 3
xn = (2*x - y) // 3
yn = n - xn

fac = [1] * (n+1)
finv = [1] * (n+1)
inv = [1] * (n+1)
def com_init(n):
    for i in range(2, n+1):
        fac[i] = fac[i - 1] * i % M
        inv[i] = M- inv[M % i] * (M // i) % M
        finv[i] = finv[i - 1] * inv[i] % M
com_init(n)
def solve(n, k):
    return fac[n] * (finv[k] * finv[n - k] % M) % M

ans = solve(n, yn)
print(ans)