A9515 | Valera and Number

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

```plain
//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 $s$ ?

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

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