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())
MOD = 10**9+7
N = 134*10**4

def power(base, num):
    if num == 0:
        return 1
    elif num % 2==0:
        return power(base, num//2) **2 % MOD
    elif num==1:
        return base % MOD
    else:
        return power(base, num//2) **2 * base % MOD
    
fact = [0 for i in range(N)]
inv_fact = [0 for i in range(N)]
 
fact[0] = 1
for i in range(1, N):
    fact[i] = fact[i-1] * i % MOD

inv_fact[N-1] = power(fact[N-1], MOD-2)
for i in range(1, N):
    inv_fact[N-1-i] = inv_fact[N-i] * (N-i) % MOD
 
def comb(x,y):
    return (fact[x] * inv_fact[y])%MOD * inv_fact[x-y] % MOD

if (2*X-Y)%3==0 and (-X+2*Y)%3==0 and 2*X-Y>=0 and -X+2*Y>=0:
    a = (2*X-Y) //3
    b = (-X+2*Y)//3
    ans = comb(a+b, min(a,b)) % MOD

    print(ans)

    
else:
    print(0)