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 (3.8.2) (judge verdict: Accepted)

def bigcmb(N, R, MOD):  # nCr(mod p) #n>=10**7,r<=10**6 #前処理不要
    if (R < 0) or (N < R):
        return 0
    R = min(R, N - R)
    fact, inv = 1, 1
    for i in range(1, R + 1):
        fact = (fact * (N - i + 1)) % MOD
        inv = (inv * i) % MOD
    return fact * pow(inv, MOD - 2, MOD) % MOD


x, y = map(int, input().split())
mod = 10 ** 9 + 7

if (x + y) % 3 != 0:
    print(0)
else:
    cnt = (x + y) // 3
    print(bigcmb(cnt, x - cnt, mod))