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)

def cmb(n,r,mod=10**9+7):
    fac = [0] * (n+1)
    finv = [0] * (n+1)
    inv = [0]*(n+1)

    fac[0] = fac[1] = 1
    finv[0] = finv[1] = 1
    inv[1] = 1
    
    for i in range(2, n+1):
        fac[i] = fac[i-1]*i % mod
        inv[i] = mod - inv[mod%i] * (mod//i) % mod
        finv[i] = finv[i-1] * inv[i] % mod

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

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

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

i = (x+y)//3
j = x-i

print(cmd(i,j))