CF441E.Valera and Number

普及/提高-

通过率：0%

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题目描述

Valera is a coder. Recently he wrote a funny program. The pseudo code for this program is given below:

//input: integers x, k, p
a = x;
for(step = 1; step <= k; step = step + 1){
    rnd = [random integer from 1 to 100];
    if(rnd <= p)
        a = a * 2;
    else
        a = a + 1;
}

s = 0;

while(remainder after dividing a by 2 equals 0){
    a = a / 2;
    s = s + 1;
}

Now Valera wonders: given the values $x$ , $k$ and $p$ , what is the expected value of the resulting number $s$ ?

输入格式

The first line of the input contains three integers $x,k,p$ ( $1<=x<=10^{9}; 1<=k<=200; 0<=p<=100$ ).

输出格式

Print the required expected value. Your answer will be considered correct if the absolute or relative error doesn't exceed $10^{-6}$ .

输入输出样例

输入#1
```
1 1 50
```
输出#1
```
1.0000000000000
```
输入#2
```
5 3 0
```
输出#2
```
3.0000000000000
```
输入#3
```
5 3 25
```
输出#3
```
1.9218750000000
```

说明/提示

If the concept of expected value is new to you, you can read about it by the link:

http://en.wikipedia.org/wiki/Expected_value

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