Purchase on credit

The bank offers a loan for purchasing a product with the following terms. If you buy a product worth S on credit for N months, your initial payment will be S/N. This is followed by monthly payments of S/N for the next N−1 months. At the end of the N months, you must pay the accumulated interest for using the credit, which is calculated as follows:

• For the first month, the interest is P·(N−1)·S/N.

• For the second month, the interest is calculated on the remaining unpaid value of the product as P·(N−2)·S/N, plus interest on the previous month's interest, which is P·P·(N−1)·S/N.

• This pattern continues for each subsequent month.

Write a program to calculate the amount of the final payment.

Input

The first line of the input contains three numbers separated by spaces: the purchase price S (an integer, 0 < S < 10^9), the number of months N (an integer, 0 < N < 100), and the interest rate P (a real number, 0 < P ≤ 0.01).

Output

Output the amount of the final payment, rounded to a precision of 10−2.

Examples