Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

D. Ilya and Escalator

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIlya got tired of sports programming, left university and got a job in the subway. He was given the task to determine the escalator load factor.

Let's assume that *n* people stand in the queue for the escalator. At each second one of the two following possibilities takes place: either the first person in the queue enters the escalator with probability *p*, or the first person in the queue doesn't move with probability (1 - *p*), paralyzed by his fear of escalators and making the whole queue wait behind him.

Formally speaking, the *i*-th person in the queue cannot enter the escalator until people with indices from 1 to *i* - 1 inclusive enter it. In one second only one person can enter the escalator. The escalator is infinite, so if a person enters it, he never leaves it, that is he will be standing on the escalator at any following second. Ilya needs to count the expected value of the number of people standing on the escalator after *t* seconds.

Your task is to help him solve this complicated task.

Input

The first line of the input contains three numbers *n*, *p*, *t* (1 ≤ *n*, *t* ≤ 2000, 0 ≤ *p* ≤ 1). Numbers *n* and *t* are integers, number *p* is real, given with exactly two digits after the decimal point.

Output

Print a single real number — the expected number of people who will be standing on the escalator after *t* seconds. The absolute or relative error mustn't exceed 10^{ - 6}.

Examples

Input

1 0.50 1

Output

0.5

Input

1 0.50 4

Output

0.9375

Input

4 0.20 2

Output

0.4

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jul/16/2019 12:16:57 (f1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|