You are a bird shooting enthusiast. You are standing on position 0 and a flock of birds (assume infinitely many birds) is flying away from you at 1m/s.
The flock of birds is initially at 1m away from you.

 

Your rating is (P, N) and your time lag is (T, R). This means the following.

 

• If P is your precision rating : At every turn, beginning when the birds are at 1m position, you take a shot at one of the birds in the flock.
  Suppose at this turn, if the flock of birds is Xm away from you, then probability that shot is successful is 1 / X^P.

• N is your range : You can only shoot at the flock of birds if it is at a distance less than or equal to N.

• T is your reload time : After every shot, you reload your gun, and that takes time T. The next time you shoot, thus the flock of birds is T more meters away than it initially was.
• R is your rejoicing time :D : If you are successful in shooting a bird, you rejoice your success and spend an extra amount of time R in reloading
  (taking a total of T + R time before the next shot).

 

Assume that you have infinitely many bullets.

 

Given N, P, T, and R. Find the expected number of birds you will shoot down!

 

Input

 

A single line containing space separated 4 numbers N, P, T, and R, in that order. P is a real number while others are positive integers.

 

Output

 

A single line containing the expected number of birds you will shoot down. The output should be correct to within 10^(-6) of the actual answer.

 

Constraints

 

• P is a real number, 1
• 1 = N = 10^18
• 1 = T = 10^5
• 1 = R = 10^5
• Further, ln(N)

 

Example

Input: 10 2 3 4 Output: 1.015625