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.