Xiao Lan likes random numbers very much.

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

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

After generating these random numbers, Xiao Ai calculates the prefix sums of the sequence to obtain the sequence $y_1, \dots, y_n$.

Given $1 \leq l \leq r \leq n$, Xiao Lan wants to know the expected number of $y_i$ that fall within the range $[l, r]$.

Input

Read the data from standard input.

A single line containing four numbers $n, p, l, r$. It is guaranteed that $1 \leq l \leq r \leq n \leq 10^9$, and the number of decimal places of $p$ does not exceed $6$.

Output

Output to standard output.

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

Examples

Input 1

3 0.5 1 2

Output 1

1.000000

Note 1

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

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

With probability $1/4$, $x_1=2$, in which case only $y_1$ falls within $[1, 2]$.

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