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 PyPy3 (2.4.0) (judge verdict: Accepted)

x, y = map(int, input().split())
if (x + y)%3 != 0:
    print(0)
else:
    k = (x + y)//3
    if k <= x <= 2*k:
        MOD = 10**9 + 7
        fac = [0]*(k + 1)
        finv = [0]*(k + 1)
        inv = [0]*(k + 1)
        fac[0] = 1; fac[1] = 1; finv[0] =1; finv[1] = 1; inv[1] = 1
        for i in range(2, k + 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
        
        i = x - k
        print(fac[k] * (finv[i] * finv[k - i] % MOD) % MOD)
    else:
        print(0)