Problem Statement

A robot is placed at the origin $(x,y)=(0,0)$ of the $xy$-plane. Initially, the robot faces the positive $x$-axis direction.

You can give this robot the following $2$ types of commands.

• G: The robot moves forward by $1$ in the direction it is facing.
• T: The robot rotates $90$ degrees counterclockwise. That is, each time this command is given, the robot's direction changes in the order positive $x$-axis → positive $y$-axis → negative $x$-axis → negative $y$-axis → positive $x$-axis → $\cdots$.

You are going to give $A$ commands G and $B$ commands T in some order (there are $\binom{A+B}{A}$ possible command orders).
Your goal is to have the robot at $(x,y)=(X,Y)$ after all $A+B$ commands have been completed.
How many command orders achieve this goal?
Since the answer can be very large, output it modulo $10^9+7$.

Input

$A\ \ B\ \ X\ \ Y$

• $0\le A,B\le 10^6$
• $A+B>0$
• $-10^6\le X,Y\le 10^6$
• All inputs are integers.

Output

Output the number of command orders such that the robot finally ends up at $(x,y)=(X,Y)$, modulo $10^9+7$.

Sample

2 1 1 1

1

1 6 0 1

2

998 244 35 3

634338670