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: Wrong Answer)


X,Y=map(int,input().split())
import math
def f2(r):

    return inv_t
def co(n,r):
    lim = 10**9 +7
    ans =1
    for i in range(1,r+1):
        ans = (ans * (n+i-1)) % lim
        
    P = 10**9 + 7
    N = r+1
    inv_t = [0]+[1]
    for i in range(2,N):
        inv_t += [inv_t[P % i] * (P - int(P / i)) % P]
        
    for i in range(1,r+1):
        ans = (ans * inv_t[i])  % lim
    return ans
def c(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
if (X+Y)%3==0:
    Z=X+Y
    if min(X,Y)-Z//3 >-1:
        #print(1)
        print(co(Z//3,min(X,Y)-Z//3))
    else:
        print(0)
else:
    print(0)