Valera and Number

2000ms

262144K

Description:

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?

Input:

The first line of the input contains three integers x, k, p (1 ≤ x ≤ 10⁹; 1 ≤ k ≤ 200; 0 ≤ p ≤ 100).

Output:

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

Sample Input:

1 1 50

Sample Output:

1.0000000000000

Sample Input:

5 3 0

Sample Output:

3.0000000000000

Sample Input:

5 3 25

Sample Output:

1.9218750000000

Note:

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

Informação

Provedor Codeforces

Código CF441E