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)

MOD = 1000000007

x,y = map(int,input().split())
if (x+y)%3!=0:
    print(0)
    exit()
p = (x+y)//3
W = x-p+1
H = y-p+1

if W == 1 or H == 1:
    print(1)
    exit()
if W < 1 or H < 1:
    print(0)
    exit()

numer = 1

inv = [0 for _ in range(max(W,H))]
inv[0] = 1

for i in range(W+H-2):
    numer *= i+1
    numer %= MOD

for i in range(1,len(inv)):
    inv[i] = inv[i-1]*pow(i+1,MOD-2,MOD) %MOD

print(numer*inv[H-2]*inv[W-2]%MOD)