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 (7.3.0) (judge verdict: Runtime Error)

#n回,m回　　X =n + 2*m  Y = 2*n + m
X,Y = map(int,input().split())
import numpy as np
a = [[1, 2], [2, 1]]
#次に逆行列を求めます。
mod = pow(10,9)+7

b = np.linalg.inv(a)


Z = np.array([[X],[Y]])

n,m=np.dot(b,Z)
p,q = *n,*m



if p<0 or q<0:
    print(0)
elif not p == int(p) or not q==int(q):
    print(0)
else:
    n = int(p)+int(q)
    
    fac = [1]*(n+1)
    for i in range(1,n+1):
        fac[i] = (fac[i-1]*i) % mod 
    print(fac[n])