小兰很喜欢随机数。

TA 首先选定了一个实数 $0 < p < 1$，然后生成了 $n$ 个随机数 $x_1,\dots,x_n$，每个数是独立按照如下方式生成的：

• $x_i$ 有 $p$ 的概率是 $1$，有 $(1-p)p$ 的概率是 $2$，有 $(1-p)^2p$ 的概率是 $3$，以此类推。

生成完这些随机数之后，小艾对这个数列求了前缀和，得到了数列 $y_1,\dots,y_n$。

给定 $1\leq l\leq r\leq n$，小兰想知道，期望有多少 $y_i$ 落在 $[l, r]$ 内？

Ran loves random numbers.

Ran first selects a real number $0 < p < 1$ and then generates $n$ random numbers $x_1,\dots,x_n$, each of which is generated independently as follows:

• $x_i$ equals to $p$ with probability $1$, $(1-p)p$ with probability $2$, $(1-p)^2p$ with probability $3$, and so on.

After generating these random numbers, Ai summed the prefixes of this series to get the series $y_1,\dots,y_n$.

Given $1\leq l\leq r\leq n$, Lan wants to know how many $y_i$ are expected to fall within $[l, r]$?

一行输入四个数 $n, p, l, r$。保证 $1\leq l\leq r\leq n\leq 10^9$，$p$ 的位数不超过 $6$。

Enter four numbers $n, p, l, r$ on a line. Ensure that $1\leq l\leq r\leq n\leq 10^9$ and $p$ has no more than $6$ digits.

输出一个实数，表示答案。你需要保证答案的绝对或相对误差不超过 $10^{-6}$。

Output a real number representing the answer. You need to ensure that the absolute or relative error of the answer does not exceed $10^{-6}$.

有 $1/4$ 的概率，$x_1=1$ 而 $x_2>1$，此时只有 $y_1$ 落在 $[1, 2]$ 内。

有 $1/4$ 的概率，$x_1=1$ 且 $x_2=1$，此时 $y_1,y_2$ 落在 $[1, 2]$ 内。

有 $1/4$ 的概率，$x_1=2$，此时只有 $y_1$ 落在 $[1, 2]$ 内。

所以期望是 $1/4\cdot (1 + 2 + 1) = 1$。

With $1/4$ probability, $x_1=1$ and $x_2>1$, only $y_1$ falls within $[1, 2]$.

With $1/4$ probability, $x_1=1$ and $x_2=1$, then $y_1,y_2$ fall in $[1, 2]$.

There is a $1/4$ probability that $x_1=2$, when only $y_1$ falls within $[1, 2]$.

So the expectation is $1/4\cdot (1 + 2 + 1) = 1$.