Problem Statement

We have a N-face die (singular of dice) that shows integers from 1 through N with equal probability.
Below, the die is said to be showing an integer X when it is placed so that the top face is the face with the integer X.
Initially, the die shows the integer S.
You can do the following two operations on this die any number (possibly zero) of times in any order.

• Pay A yen (the Japanese currency) to "increase" the value shown by the die by 1, that is, reposition it to show X+1 when it currently shows X. This operation cannot be done when the die shows N.
• Pay B yen to recast the die, after which it will show an integer between 1 and N with equal probability.

Consider making the die show T from the initial state where it shows S.
Print the minimum expected value of the cost required to do so when the optimal strategy is used to minimize this expected value.

Input

Input is given from Standard Input in the following format:
N S T A B

Output

Print the answer.
Your output will be considered correct when its absolute or relative error is at most 10^{-5}.

Constraints

• $1 \leq N \leq 10^9$
• $1 \leq S, T \leq N$
• $1 \leq A, B \leq 10^9$
• All values in input are integers.

Sample Input 1

5 2 4 10 4

Sample Output 1

15.0000000000000000

When the optimal strategy is used to minimize the expected cost, it will be 15 yen.

Sample Input 2

10 6 6 1 2

Sample Output 2

0.0000000000000000

The die already shows T in the initial state, which means no operation is needed.

Sample Input 3

1000000000 1000000000 1 1000000000 1000000000

Sample Output 3

1000000000000000000.0000000000000000

Your output will be considered correct when its absolute or relative error is at most 10^{-5}.

见题面 Input 部分

见题面 Output 部分