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)

# 逆元
# a^n mod を計算する
def modpow(a, n, mod):
    res = 1
    while n > 0:
        if n & 1:
            res = res * a % mod
        a = a * a % mod
        n >>= 1
    return res

# a^{-1} mod を計算する
def modinv(a, mod):
    return modpow(a, mod - 2, mod)


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

mod = 10 ** 9 + 7

if (x + y) % 3 == 0 and min(x, y) * 2 >= max(x, y):
    a = (2 * y - x) // 3
    b = (2 * x - y) // 3
    x = 1
    for i in range(2, a + b + 1):
        x = x * i % mod
    for i in range(2, a + 1):
        x = x * modinv(i, mod) % mod
    for i in range(2, b + 1):
        x = x * modinv(i, mod) % mod
    print(x)
else:
    print(0)