# Circles of Waiting

## 题目描述

A chip was placed on a field with coordinate system onto point \$ (0,0) \$ . Every second the chip moves randomly. If the chip is currently at a point \$ (x,y) \$ , after a second it moves to the point \$ (x-1,y) \$ with probability \$ p_{1} \$ , to the point \$ (x,y-1) \$ with probability \$ p_{2} \$ , to the point \$ (x+1,y) \$ with probability \$ p_{3} \$ and to the point \$ (x,y+1) \$ with probability \$ p_{4} \$ . It's guaranteed that \$ p_{1}+p_{2}+p_{3}+p_{4}=1 \$ . The moves are independent. Find out the expected time after which chip will move away from origin at a distance greater than \$ R \$ (i.e. ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF963E/246aa7b086b7ae016d999e705d5862993be04853.png) will be satisfied).

## 输入输出格式

### 输入格式

First line contains five integers \$ R,a_{1},a_{2},a_{3} \$ and \$ a_{4} \$ ( \$ 0<=R<=50,1<=a_{1},a_{2},a_{3},a_{4}<=1000 \$ ). Probabilities \$ p_{i} \$ can be calculated using formula ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF963E/f4c10e1f02852c4316fc9bec25d03186d7840bcb.png).

### 输出格式

It can be shown that answer for this problem is always a rational number of form ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF963E/ed2c29110477df816fcacba17d99273426c4dd91.png), where ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF963E/2a1de71f5127e0ac869e59f9af51dec4e82446fc.png). Print \$ P·Q^{-1} \$ modulo \$ 10^{9}+7 \$ .

## 输入输出样例

### 输入样例 #1

``````0 1 1 1 1
``````

### 输出样例 #1

``1``

### 输入样例 #2

``````1 1 1 1 1
``````

### 输出样例 #2

``666666674``

### 输入样例 #3

``````1 1 2 1 2
``````

### 输出样例 #3

``538461545``

## 说明

In the first example initially the chip is located at a distance \$ 0 \$ from origin. In one second chip will move to distance \$ 1 \$ is some direction, so distance to origin will become \$ 1 \$ . Answers to the second and the third tests: ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF963E/1afdb873d5404107498744fbaddde38ee83fd279.png) and ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF963E/4c1b0d15ba2866c8474bd814731c993c182c0d7d.png).