Bernoulli scheme

Let us consider the Bernoulli trial scheme.

There are $n$ independent trials. The probability of event $A$ occurring in each trial is $p$. Find the probability that in $n$ independent trials, event $A$ will occur exactly $k$ times.

Input

The first line contains two integers: $n(0<n\le 15)$ and $k(0\le k\le n)$

The second line contains one real number $p(0\le p\le 1)$.

Output

Print the probability that in $n$ independent trials, event $A$ will occur exactly $k$ times. Print the answer with at least $6$ decimal places.

Examples