Mr. Tan aims to earn X VND before retiring. Upon retirement, he plans to put the entire X VND into a safe investment with a stable monthly return of r%. At the end of the first month, he plans to withdraw Y VND for expenses. Due to the impact of inflation with an monthly rate of f%, in the following months, he will withdraw an amount of money that ensures a standard of living equivalent to the Y VND from the first month of retirement. Mr. Tan wants to ensure that he has enough money to spend for at least N months (i.e. Mr. Tan withdraws N-1 times).

Input

The only line contain 2 real numbers r and f, and 2 integers Y and N

Output

Calculate X (rounded to 4 decimal places)

Example

Input

0.6 0.25 20 400

Output

4291.8397