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: Time Limit Exceeded)

# 73

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

a = 2*y - x
b = 2*x - y

fac_l = [0] * (int((a + b) / 3) + 1)
inv_l = [0] * (int((a + b) / 3) + 1)
finv_l = [0] * (int((a + b) / 3) + 1)


def com_init():
    fac_l[1] = 1
    inv_l[0] = 1
    inv_l[1] = 1
    finv_l[0] = 1
    finv_l[1] = 1
    for i in range(2, a+b+1):
        fac_l[i] = (fac_l[i-1] * i) % MOD
        inv_l[i] = MOD - (inv_l[MOD % i] * int(MOD / i)) % MOD
        finv_l[i] = finv_l[i-1] * inv_l[i]


def ncr(n, r):
    return (((fac_l[n] * finv_l[r]) % MOD) * finv_l[n-r]) % MOD


if a % 3 != 0 or b % 3 != 0:
    print("0")
else:
    a = int(a/3)
    b = int(b/3)

    com_init()
    print(ncr(a+b, a))