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 (3.4.3) (judge verdict: Runtime Error)

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

MOD = int(1.0e+9 + 7)
DP_max = 3333334

DP = []
if(2 * y - x) % 3 != 0 or (2 * x - y) % 3 != 0:
    print(0)

if(2 * y - x) < 0 or (2 * x - y) < 0:
    print(0)

X = int((2 * y - x) / 3)
Y = int((2 * x - y) / 3)

for i in range(X + 1):
    DP.append([1])

for i in range(Y + 1):
    DP[0].append(1)


for i in range(1, X + 1):
    for j in range(1, Y + 1):
        DP[i].append((DP[i][j - 1] + DP[i - 1][j]) % MOD)

print(DP[X][Y])