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: Runtime Error)

x,y = map(int,input().split())
mod = 10**9 + 7
if (x+y)%3 != 0:
    print(0)
    exit()
n = (x+y)//3
a = (2 * x - y) // 3
b = (2 * y - x) // 3
if a == 0 or b == 0:
    print(1)
    exit()
if a < 0 or b < 0:
    print(0)
    exit()
MAX = 10
fac = [1,1] + [0] * MAX
finv = [1,1] + [0] * MAX
inv = [0,1] + [0] * MAX
for i in range(2,MAX):
    fac[i] = fac[i-1] * i % mod
    inv[i] = -inv[mod%i] * (mod // i) % mod
    finv[i] = finv[i-1] * inv[i]%mod


def nCr(n,r):
    if n<r:
        return 0
    if n<0 or r<0:
        return 0
    return fac[n] * (finv[r] * finv[n-1]%mod)%mod

print(nCr(n,a))