CF963E.Circles of Waiting

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. will be satisfied).

一枚芯片被放置在带有坐标系的平面上的点 $(0,\,0)$ 处。

每一秒，该芯片随机移动一次。若芯片当前位于点 $(x,\,y)$，则经过一秒后，它将以概率 $p_1$ 移动到点 $(x-1,\,y)$，以概率 $p_2$ 移动到点 $(x,\,y-1)$，以概率 $p_3$ 移动到点 $(x+1,\,y)$，以概率 $p_4$ 移动到点 $(x,\,y+1)$。已知 $p_1 + p_2 + p_3 + p_4 = 1$。各次移动相互独立。

求芯片首次离开原点距离超过 $R$（即满足 ）的期望时间。

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 .

第一行包含五个整数 $R$、$a_1$、$a_2$、$a_3$ 和 $a_4$（其中 $0 \leq R \leq 50$，$1 \leq a_1, a_2, a_3, a_4 \leq 1000$）。

概率 $p_i$ 可通过公式 计算。

It can be shown that answer for this problem is always a rational number of form , where .

Print P·Q - 1 modulo 109 + 7.

可以证明，本题的答案总是一个形如 的有理数，其中 。

请输出 $ P \cdot Q^{-1} \bmod (10^9 + 7) $。

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: and .

在第一个例子中，芯片初始时位于距原点距离为 0 的位置。一秒后，芯片将向某个方向移动至距原点距离为 1 的位置，因此其到原点的距离变为 1。

第二和第三个测试用例的答案分别为： 和 。