Robot

A robot stands at the origin of the xy plane. It faces the positive x direction, and from now on it makes $N$ moves. One move works like this.

1. The robot turns 90 degrees to the left of its facing with probability $\frac{L}{L+M+R}$, keeps its facing with probability $\frac{M}{L+M+R}$, and turns 90 degrees to the right of its facing with probability $\frac{R}{L+M+R}$. From the starting state, a left turn makes it face the positive y direction and a right turn makes it face the negative y direction.
2. Once the facing is settled, the robot moves a distance of 1 in that direction.

If the robot ends up at $(x, y)$ after $N$ moves, how far it sits from the origin is measured by $x^2 + y^2$. Write a program that computes the expected value of that measure after the robot makes $N$ moves.

The first line contains four integers $N$, $L$, $M$, $R$ separated by spaces. $N$ is the number of moves the robot makes, and $L$, $M$, $R$ determine the probability of turning left, of keeping the facing, and of turning right. At least one of $L$, $M$, $R$ is a positive integer. ($1 \le N \le 10^9$, $0 \le L, M, R \le 10^6$)

Print the expected value of how far the robot sits from the origin after $N$ moves. For exact judging, write the answer as a reduced fraction $a/b$ and print the remainder of $a \times b^{-1}$ divided by 1,000,000,007 instead. Here $b^{-1}$ is the multiplicative inverse of $b$ modulo 1,000,000,007. The answer exists for every input that can be given in this problem.