10794: ABC145 - D - Knight
[Creator : ]
Description
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 $10^9 + 7$.
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 $10^9 + 7$.
Input
Input is given from Standard Input in the following format:
```
$X$ $Y$
```
```
$X$ $Y$
```
Output
Print the number of ways for the knight to reach $(X, Y)$ from $(0, 0)$, modulo $10^9 + 7$.
Constraints
- $1 \leq X \leq 10^6$
- $1 \leq Y \leq 10^6$
- All values in input are integers.
- $1 \leq Y \leq 10^6$
- All values in input are integers.
Sample 1 Input
3 3
Sample 1 Output
2
There are two ways: $(0,0) \to (1,2) \to (3,3)$ and $(0,0) \to (2,1) \to (3,3)$.
Sample 2 Input
2 2
Sample 2 Output
0
The knight cannot reach $(2,2)$.
Sample 3 Input
999999 999999
Sample 3 Output
151840682
Print the number of ways modulo $10^9 + 7$.